Borderline gradient continuity for nonlinear parabolic systems

被引：15

作者：

Kuusi, Tuomo ^{[1
]}

Mingione, Giuseppe ^{[2
]}

机构：

[1] Aalto Univ, Dept Math & Syst Anal, Aalto 00076, Finland

[2] Univ Parma, Dipartimento Matemat & Informat, Parco Area Sci 53-A, I-43124 Parma, Italy

来源：

MATHEMATISCHE ANNALEN | 2014年 / 360卷 / 3-4期

基金：

芬兰科学院;

关键词：

REGULARITY; EQUATIONS; DIFFERENTIABILITY; BOUNDEDNESS;

D O I：

10.1007/s00208-014-1055-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the evolutionary -Laplacean system in cylindrical domains of , and prove the continuity of the spatial gradient under the Lorentz space assumption . When is time independent the condition improves in . This is the limiting case of a result of DiBenedetto claiming that is Holder continuous when for . At the same time, this is the natural nonlinear parabolic analog of a linear result of Stein, claiming the gradient continuity of solutions to the linear elliptic system is continuous. New potential estimates are derived and moreover suitable nonlinear potentials are used to describe fine properties of solutions.

引用

页码：937 / 993

页数：57

共 38 条

[1] Gradient estimates for a class of parabolic systems
Acerbi, Emilio
Mingione, Giuseppe
[J]. DUKE MATHEMATICAL JOURNAL, 2007, 136 (02) : 285 - 320
[2] [Anonymous], 1992, J. Geom. Anal.
[3] [Anonymous], 1972, Russian Math. Surveys, DOI 10.1070/RM1972v027n06ABEH001393
[4] Baroni P., 2012, THESIS
[5] Nonlinear parabolic equations with measure data
Boccardo, L
DallAglio, A
Gallouet, T
Orsina, L
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1997, 147 (01) : 237 - 258
[6] Global Boundedness of the Gradient for a Class of Nonlinear Elliptic Systems
Cianchi, Andrea
Maz'ya, Vladimir G.
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2014, 212 (01) : 129 - 177
[7] Global Lipschitz Regularity for a Class of Quasilinear Elliptic Equations
Cianchi, Andrea
Maz'ya, Vladimir G.
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2011, 36 (01) : 100 - 133
[8] DIBENEDETTO E, 1985, J REINE ANGEW MATH, V357, P1
[9] DiBenedetto E., 1993, Degenerate parabolic equations, DOI [10.1007/978-1-4612-0895-2, DOI 10.1007/978-1-4612-0895-2]
[10] Harnack estimates for quasi-linear degenerate parabolic differential equations
DiBenedetto, Emmanuele
Gianazza, Ugo
Vespri, Vincenzo
[J]. ACTA MATHEMATICA, 2008, 200 (02) : 181 - 209

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