Publications

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, C. Scheven, and L. Schätzler. 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.
  • V. Bögelein, T. Stanin. The one-sided bounded slope condition in evolution problems,  Ann. Mat. Pura Appl. (4), to appear, 2019. 

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, 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, C. Scheven, and T. Singer. Existence of variational solutions in non-cylindrical domains,  SIAM J. Math. Anal., 50(3), 3007-3057, 2018.

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.

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.

2015

  • V. Bögelein. Partial boundary regularity of non-linear parabolic systems in low dimensions.  Analysis (Berlin). 35:1-28, 2015.
  • V. Bögelein. Global gradient bounds for the parabolic p-Laplacian system,  Proc. London Math. Soc. 111(3):633-680, 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. Short-time regularity for the H-surface-flow.  Int. Math. Res. Not. IMRN. 12:3694-3750, 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, T. Lukkari and C. Scheven. The obstacle problem for the porous medium equation.  Math. Ann.  363(1), 455-499, 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.
  • 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, F. Duzaar and P. Marcellini. Existence of evolutionary variational solutions via the calculus of variations.  J. Differential Equations. 256(12):3912-3942, 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.

 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.

 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.  Math. Ann. 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.

 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

 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

  • 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.