Publikationen der Arbeitsgruppe Analysis

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• 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: $\epsilon$-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.
• 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 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.