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

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

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.