Publikationen der Arbeitsgruppe Analysis
- K. Moring and R. Rainer. Stability for systems of porous medium type. J. Math. Anal. Appl., 506(1), 125532, 2022.
- N. Liao and L. Schätzler. On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part III. Int. Math. Res. Not. IMRN, 2022(3):2376-2400, 2022.
- V. Bögelein, N. Dietrich and M. Vestberg. Existence of solutions to a diffusive shallow medium equation. J. Evol. Equ. 21:845-889, 2021.
- V. Bögelein, F. Duzaar and N. Liao. On the Hölder regularity of signed solutions to a doubly nonlinear equation. J. Funct. Anal. 281(9), 2021.
- V. Bögelein, A. Herán, L. Schätzler and T. Singer. Harnack’s inequality for doubly nonlinear equations of slow diffusion type. Calc. Var. Partial Differential Equations, 60, 215, 2021.
- U. Gianazza and N. Liao. Continuity of the temperature in a multi-phase transition problem. Math. Ann. 1-35, 2021.
- N. Liao. Hölder regularity for porous medium systems. Calc. Var. Partial Differential Equations, 60, 156, 2021.
- N. Liao. Regularity of weak supersolutions to elliptic and parabolic equations: Lower semicontinuity and pointwise behavior. J. Math. Pures Appl., 147:179–204, 2021.
- N. Liao. Remarks on parabolic De Giorgi classes. Ann. di Mat. Pura ed Appl., 2021.
- R. Rainer, J. Siltakoski and T. Stanin. An evolutionary Haar-Rado type theorem. Manuscripta Math., 2021.
- L. Schätzler. The obstacle problem for degenerate doubly nonlinear equations of porous medium type. Ann. di Mat. Pura ed Appl., 200(2):641-683, 2021.
- T. Stanin. Global continuity of variational solutions weakening the one-sided bounded slope condition. Forum Math., 2021.
- S. Blatt. The gradient flow of the Möbius energy: -regularity and consequences. Anal. PDE, 13(3):901-941, 2020.
- V. Bögelein, B. Dacorogna, F. Duzaar, P. Marcellini and C. Scheven. Integral convexity and parabolic systems. SIAM J. Math. Anal., 52(2):1489–1525, 2020.
- V. Bögelein, F. Duzaar, J. Kinnunen und C. Scheven. Higher integrability for doubly nonlinear parabolic systems. J. Math. Pures Appl., 143:31–72, 2020.
- V. Bögelein, F. Duzaar und C. Scheven. Higher integrability for the singular porous medium system. J. Reine Angew. Math., 2020(767):203–230, 2020.
- V. Bögelein and T. Stanin. The one-sided bounded slope condition in evolution problems. Ann. di Mat. Pura ed Appl., 199(2):573–587, 2020.
- U. Gianazza and N. Liao. A boundary estimate for degenerate parabolic diffusion equations. Potential Analysis, 53:977-995, 2020.
- U. Gianazza and N. Liao. A boundary estimate for singular sub-critical parabolic equations. Int. Math. Res. Not. IMRN, 2020.
- N. Liao, I. Skrypnik und V. Vespri. Local regularity for an anisotropic elliptic equation. Calc. Var. Partial Differential Equations, 59, 116, 2020.
- N. Liao. A unified approach to the Hölder regularity of solutions to degenerate and singular parabolic equations. J. Differential Equations, 268(10):5704-5750, 2020.
- L. Schätzler. The obstacle problem for singular doubly nonlinear equations of porous medium type. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 31(3):503–548, 2020.
- N. Vorderobermeier. On the regularity of critical points for O’Hara’s knot energies: From smoothness to analyticity. Commun. Contemp. Math., 1–28, 2020.
- S. Blatt. A note on singularities in finite time for the L2-gradient flow of the Helfrich functional, Journal of Evolution Equations, online first, 2019.
- S. Blatt. Curves between Lipschitz and C1 and their relation to geometric knot theory, Journal of Geometric Analysis, 29:3270–3292, 2019.
- S. Blatt and N. Vorderobermeier. On the analyticity of critical points of the Möbius energy, Calc. Var. Partial Differential Equations, 58(1):58:16, 2019.
- V. Bögelein, F. Duzaar, R. Korte and C. Scheven. The higher integrability of weak solutions of porous medium systems, Adv. Nonlinear Anal., 8(1):1004-1034, 2019.
- V. Bögelein, F. Duzaar, L. Schätzler and C. Scheven. Existence for evolutionary problems with linear growth by stability methods, J. Differential Equations, 266:7709-7748, 2019.
- V. Bögelein, P. Lehtelä and S. Sturm. Regularity of weak solutions and supersolutions to the Porous Medium Equation, Nonlinear Anal., 185:49-67, 2019.
- R. Korte, P. Lehtelä and S. Sturm. Lower semicontinuous obstacles for the porous medium equation, J. Differential Equations, 266(4):1851-1864, 2019.
- N. Liao. A sufficient condition for the continuity of solutions to a logarithmic diffusion equation. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), XIX(3):1161-1184, 2019.
- L. Schätzler. Existence for evolutionary Neumann problems with linear growth by stability results. Ann. Acad. Sci. Fenn. Math., 2019(44):1055–1092, 2019.
- L. Schätzler. Existence for singular doubly nonlinear systems of porous medium type with time dependent boundary values. J. Elliptic Parabol. Equ., 2019(5):383–421, 2019.
2018
- S. Blatt, The gradient flow of O’Hara’s knot energies, Math. Ann. 370(3-4):993–1061, 2018.
- V. Bögelein, F. Duzaar, P. Marcellini and C. Scheven. A variational approach to doubly nonlinear equations, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 29:739-772, 2018.
- V. Bögelein, F. Duzaar, P. Marcellini and C. Scheven. Doubly Nonlinear Equations of Porous Medium Type, Arch. Ration. Mech. Anal. 229:503–545, 2018.
- V. Bögelein, F. Duzaar, C. Scheven and T. Singer. Existence of variational solutions in non-cylindrical domains, SIAM J. Math. Anal., 50(3), 3007-3057, 2018.
- U. Gianazza, N. Liao and T. Lukkari. A boundary estimate for singular parabolic diffusion equations. NoDEA Nonlinear Differential Equations Appl. 25, 33, 2018.
- C. Klaus and N. Liao. A short proof of Hölder continuity for functions in DeGiorgi classes. Ann. Acad. Sci. Fenn. Math., 43:931-934, 2018.
- S. Sturm. Pointwise estimates via parabolic potentials for a class of doubly nonlinear parabolic equations with measure data, Manuscripta Math. 157:295-322, 2018.
2017
- S. Blatt. Monotonicity formulas for extrinsic triharmonic maps and the triharmonic Lane–Emden equation, J. Differential Equations. 262(12):5691-5734, 2017.
- V. Bögelein, F. Duzaar and N. Fusco. A quantitative isoperimetric inequality on the sphere, Adv. Calc. Var., 10(3):223-265, 2017.
- V. Bögelein, F. Duzaar, P. Marcellini and S. Signoriello. Parabolic equations and the bounded slope condition, Ann. Inst. H. Poincaré, Anal. Non Linéaire. 34(2):355-379, 2017.
- V. Bögelein, F. Duzaar and C. Scheven. The obstacle problem for parabolic minimizers, J. Evol. Equ., 17(4):1273-1310, 2017.
- V. Bögelein, T. Lukkari and C. Scheven. Hölder regularity for degenerate parabolic obstacle problems, Ark. Mat., 55:1-39, 2017.
- V. Bögelein, F. Ragnedda, S. Vernier Piro and V. Vespri. Moser-Nash kernel estimates for degenerate parabolic equations, J. Funct. Anal. 272(7):2956-2986, 2017.
- L. Schätzler. Existence of variational solutions for time dependent integrands via minimizing movements. Analysis (Germany), 37(4):199–222, 2017.
- S. Signoriello and T. Singer. Hölder continuity of parabolic quasi-minimizers, J. Differential Equations, 263(9):6066-6114, 2017.
- S. Sturm. Existence of very weak solutions of doubly nonlinear parabolic equations with measure data, Ann. Acad. Sci. Fenn. Math. 42:931-962, 2017.
- S. Sturm. Existence of weak solutions of doubly nonlinear parabolic equations, J. Math. Anal. Appl. 455:842-863, 2017.
2016
- S. Blatt, P. Reiter and A. Schikorra. Harmonic analysis meets critical knots. Critical points of the Möbius energy are smooth. Trans. Amer. Math. Soc., 368:6391-6438, 2016.
- S. Blatt and M. Struwe. Well-posedness of the supercritical Lane-Emden heat flow in Morrey spaces, ESAIM: Control, Optimisation and Calculus of Variations, 22(4):1370-1381, 2016.
- V. Bögelein, F. Duzaar and U. Gianazza. Sharp boundedness and continuity results for the singular porous medium equation, Israel J. Math. 214:259-314, 2016.
- V. Bögelein, F. Duzaar, and C. Scheven. The obstacle problem for the total variation flow, Ann. Sci. Éc. Norm. Supér. 49(5):1143–1188, 2016.
- V. Bögelein, F. Duzaar, and C. Scheven. The total variation flow with time dependent boundary values, Calc. Var. Partial Differential Equations, 55:108, 2016.
- T. Singer. Existence of weak solutions of parabolic systems with p,q-growth, Manuscripta Math. 151, 87–112, 2016.
- T. Singer. Local Boundedness of variational solutions to evolutionary problems with non-standard growth, NoDEA Nonlinear Differential Equations Appl., 23:19, 2016.
2015
- S. Blatt and P. Reiter. Regularity theory for tangent-point energies: The non-degenerate sub-critical case, Adv. Calc. Var. 8(2):93–116, 2015.
- S. Blatt and P. Reiter. Towards a regularity theory for integral Menger curvature, Ann. Acad. Sci. Fenn., Math. 40:149–181, 2015.
- S. Blatt and M. Struwe. An analytic framework for the supercritical Lane-Emden equation and its gradient flow, Int. Math. Res. Not. IMRN. 2015 (9): 2342-2385, 2015.
- S. Blatt and M. Struwe. Boundary Regularity for the supercritical Lane-Emden heat flow, Calc. Var. Partial Differential Equations. 54(2): 2269-2284, 2015.
- V. Bögelein. Global gradient bounds for the parabolic p-Laplacian system, Proc. London Math. Soc. 111(3):633-680, 2015.
- V. Bögelein. Partial boundary regularity of non-linear parabolic systems in low dimensions, Analysis (Berlin). 35:1-28, 2015.
- V. Bögelein, F. Duzaar and N. Fusco. A sharp quantitative isoperimetric inequality in higher codimension, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 26(3):309-362, 2015.
- V. Bögelein, F. Duzaar and U. Gianazza. Very weak solutions of singular porous medium equations with measure data. Commun. Pure Appl. Anal. 14(1):23-49, 2015.
- V. Bögelein, F. Duzaar and P. Marcellini. A time dependent variational approach to image restoration, SIAM J. Imaging Sci. 8(2):968-1006, 2015.
- V. Bögelein, F. Duzaar, P. Marcellini, and S. Signoriello. Nonlocal diffusion equations, J. Math. Anal. Appl. 432(1):398-428, 2015.
- V. Bögelein, F. Duzaar and C. Scheven. A sharp quantitative isoperimetric inequality in hyperbolic n-space, Calc. Var. Partial Differential Equations, 54(3):3967-4017, 2015.
- V. Bögelein, F. Duzaar and C. Scheven. Short-time regularity for the H-surface-flow. Int. Math. Res. Not. IMRN. 12:3694-3750, 2015.
- V. Bögelein, T. Lukkari and C. Scheven. The obstacle problem for the porous medium equation, Math. Ann. 363(1), 455-499, 2015.
- N. Liao. Existence and nonexistence of solutions to a logarithmic diffusion equation in bounded domains. Manuscripta Math., 147:101-138, 2015.
- S. Signoriello and T. Singer. Local Calderón-Zygmund estimates for parabolic minimizers, Nonlinear Anal. 125: 561–581, 2015.
- T. Singer. Parabolic equations with p,q-growth: The subquadratic case. Q. J. Math. 66 (2): 707-742, 2015.
- S. Sturm. Pointwise estimates for porous medium type equations with low order terms and measure data. Electron. J. Diff. Equ. 2015:1-25, 2015.
2014
- P. Baroni and V. Bögelein. Calderón-Zygmund estimates for parabolic p(x,t)-Laplacian systems, Rev. Mat. Iberoam. 30(4):1355-1386, 2014.
- S. Blatt and P. Reiter. How nice are critical knots? Regularity theory for knot energies. Journal of Physics: Conference Series, 544, published online, 2014.
- S. Blatt and P. Reiter. Modeling repulsive forces on fibres via knot energies, Mol. Based Math. Biol. 2(1):56-72, 2014.
- V. Bögelein. Global Calderón & Zygmund theory for nonlinear parabolic systems. Calc. Var. Partial Differential Equations. 51(3-4):555-596, 2014.
- V. Bögelein, F. Duzaar and U. Gianazza. Continuity estimates for porous medium type equations with measure data. J. Funct. Anal. 267:3351-3396, 2014.
- V. Bögelein and Q. Li. Very weak solutions of degenerate parabolic systems with non-standard p(x,t)-growth. Nonlinear Anal. 98:190-225, 2014.
- V. Bögelein, F. Duzaar and P. Marcellini. Existence of evolutionary variational solutions via the calculus of variations. J. Differential Equations. 256(12):3912-3942, 2014.
- E. DiBenedetto, U. Gianazza and N. Liao. Two remarks on the local behavior of solutions to logarithmically singular diffusion equations and its porous-medium type approximations. Riv. Mat. Univ. Parma, 5(1):139-182, 2014.
2013
- S. Blatt. A note on Integral Menger Curvature. Math. Nachr. 286(2-3):149-159, 2013.
- S. Blatt. The Energy space of the Tangent Point Energies. J. Topol. Anal. 5(3):261-270, 2013.
- S. Blatt and P. Reiter. Stationary Points of O’Hara’s Knot Energies. Manuscripta Math. 140(1-2):29-50, 2013.
- V. Bögelein, F. Duzaar and U. Gianazza. Porous medium type equations with measure data and potential estimates. SIAM J. Math. Anal. 45(6):3283-3330, 2013.
- V. Bögelein, F. Duzaar and P. Marcellini. Parabolic equations with p,q-growth. J. Math. Pures Appl. 100(4):535-563, 2013.
- V. Bögelein, F. Duzaar and P. Marcellini. Parabolic systems with p,q-growth: A variational approach. Arch. Ration. Mech. Anal. 210(1):219-267, 2013.
- V. Bögelein, F. Duzaar and G. Mingione. The regularity of general parabolic systems with degenerate diffusions. Mem. Amer. Math. Soc. 221(1041), 2013.
- V. Bögelein, F. Duzaar and C. Scheven. Weak solutions to the heat flow for surfaces of prescribed mean curvature. Trans. Amer. Math. Soc. 365:4633-4677, 2013.
- M. Revers. On the asymptotics of polynomial interpolation for |x|α at the Chebyshev nodes. J. Approx. Theory 165; 70-82, 2013.
2012
- S. Blatt. Boundedness and Regularizing Effects of O’Hara’s Knot Energies. J. Knot Theory Ramifications. 21(1), 9 pages, 2012.
- S. Blatt. The Gradient Flow of the Möbius Energy near local Minimizers. Calc. Var. Partial Differential Equations. 43(3-4):403-439, 2012.
- S. Blatt and S. Kolasinski. Sharp Boundedness and Regularizing effects of the integral Menger curvature for submanifolds. Adv. Math. 230(3):839-852, 2012.
- V. Bögelein. Partial regularity for minimizers of discontinuous quasiconvex integrals with degeneracy. J. Differential Equations. 252(2):1052-1100, 2012.
- V. Bögelein and F. Duzaar. Hölder estimates for parabolic p(x,t)-Laplacian systems. Mathematische Annalen. 354(3):907-938, 2012.
- V. Bögelein, F. Duzaar, J. Habermann and C. Scheven. Stationary electro-rheological fluids: Low order regularity for systems with discontinuous coefficients. Adv. Calc. Var. 5(1):1-57, 2012.
- V. Bögelein, F. Duzaar and C. Scheven. Global solutions to the heat flow for m-harmonic maps and regularity. Indiana Univ. Math. J. 61(6):2157-2210, 2012.
- V. Bögelein, M. Foss and G. Mingione. Regularity in parabolic systems with continuous coefficients. Math. Z. 270(3-4):903-938, 2012.
- V. Bögelein and C. Scheven. Higher integrability in parabolic obstacle problems. Forum Math. 24(5):931–972, 2012.
- E. DiBenedetto, U. Gianazza and N. Liao. Logarithmically singular parabolic equations as limits of the porous medium equation. Nonlinear Anal., 75(12):4513-4533, 2012.
- E. DiBenedetto, U. Gianazza and N. Liao. On the local behavior of non-negative solutions to a logarithmically singular equation. Discrete Contin. Dyn. Syst. Ser. B, 17(6):1841-1858, 2012.
2011
- V. Bögelein and F. Duzaar. Higher integrability for parabolic systems with non-standard growth and degenerate diffusions. Publ. Mat. 55(1):201-250, 2011.
- V. Bögelein, F. Duzaar, J. Habermann and C. Scheven. Partial Hölder continuity for discontinuous elliptic problems with VMO-coefficients. Proc. London Math. Soc. 103(3):371-404, 2011.
- V. Bögelein, F. Duzaar and G. Mingione. Degenerate problems with irregular obstacles. J. Reine Angew. Math. 650:107-160, 2011.
2010
- S. Blatt. Loss of convexity and embeddedness for geometric evolution equations of higher order. J. Evol. Equ. 10(1):21-27, 2010.
- V. Bögelein, F. Duzaar and G. Mingione. The boundary regularity of non-linear parabolic systems I. Ann. Inst. H. Poincaré, Anal. Non Linéaire 27(1):201-255, 2010.
- V. Bögelein, F. Duzaar and G. Mingione. The boundary regularity of non-linear parabolic systems II. Ann. Inst. H. Poincaré, Anal. Non Linéaire 27(1):145-200, 2010.
- V. Bögelein and J. Habermann. Gradient estimates via non standard potentials and continuity. Ann. Acad. Sci. Fenn. Math. 35:641-678, 2010.
- V. Bögelein and M. Parviainen. Self-improving property of nonlinear higher order parabolic systems near the boundary. Nonlinear Differ. Equ. Appl. 17(1):21-54, 2010.
2009
- S. Blatt. A singular example for the Willmore flow. Analysis (Oldenbourg) 29(4):407–430, 2009.
- S. Blatt. Chord-arc constants for submanifolds of arbitrary codimension. Adv. Calc. Var. 2(3):271–309, 2009.
- S. Blatt, H.-P. Blatt and W. Luh. On a generalization of Jentzsch’s theorem. J. Approx. Theory. 159(1):26–38, 2009.
- V. Bögelein. Partial regularity and singular sets of solutions of higher order parabolic systems. Ann. Mat. Pura Appl. 188(1):61-122, 2009.
- V. Bögelein. Very weak solutions of higher order degenerate parabolic systems. Advances in Differential Equations. 14(1-2):121-200, 2009.
2008
- S. Blatt and P. Reiter. Does finite knot energy lead to differentiability? J. Knot Theory Ramifications. 17(10):1281–1310, 2008.
- V. Bögelein. Higher integrability for weak solutions of higher order degenerate parabolic systems. Ann. Acad. Sci. Fenn., Math. 33(2):387-412, 2008.
2007
- V. Bögelein and A. Zatorska-Goldstein. Higher integrability of very weak solutions of systems of p(x)-Laplacean type. J. Math. Anal. Appl. 336(1):480-497, 2007.
2004
- M. Revers and M. Ganzburg. A note on Lagrange Interpolation for |x|α at equidistant nodes. Bull. Austral. Math. Soc. 70:475-480, 2004.
2001
- M. Revers. On Lagrange interpolation for functions of bounded variation. Math. Pannon. 12(1):133-138, 2001.
2000
- M. Revers. Approximation constants in equidistant Lagrange interpolation. Period. Math. Hungar. 40(2):167-175, 2000.
- M. Revers. On Lagrange interpolation with equally spaced Nodes. Bull. Austral. Math. Soc. 62(3):357-368, 2000.
- M. Revers. On Lagrange interpolatory parabolas to | x|α at equally spaced nodes. Arch. Math. 74(5):385-391, 2000.
- M. Revers. On the zero-divergence of equidistant Lagrange interpolation. Monatsh. Math. 131(3):215-221, 2000.
- M. Revers. The divergence of Lagrange interpolation for |x|α at equidistant nodes. J. Approx. Theory. 103:269-280, 2000.