Gradient bounds for anisotropic partial differential equations

被引：18

作者：

Farina, Alberto ^{[1
]}

Valdinoci, Enrico ^{[2
]}

机构：

[1] Univ Picardie Jules Verne, Fac Sci, LAMFA, CNRS UMR 6140, F-80039 Amiens 1, France

[2] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2014年 / 49卷 / 3-4期

关键词：

UNBOUNDED-DOMAINS; REGULARITY;

D O I：

10.1007/s00526-013-0605-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider solutions in the whole of the space of a partial differential equation driven by the anisotropic Laplacian. We prove a pointwise energy bound and we derive from that some rigidity results.

引用

页码：923 / 936

页数：14

共 17 条

[1] Convex symmetrization and applications
Alvino, A
Ferone, V
Trombetti, G
Lions, PL
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1997, 14 (02): : 275 - 293
[2] [Anonymous], 1968, LINEAR QUASILINEAR E
[3] [Anonymous], 1981, MATH SCI ENG
[4] A GRADIENT BOUND FOR ENTIRE SOLUTIONS OF QUASI-LINEAR EQUATIONS AND ITS CONSEQUENCES
CAFFARELLI, L
GAROFALO, N
SEGALA, F
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1994, 47 (11) : 1457 - 1473
[5] A POINTWISE GRADIENT ESTIMATE FOR SOLUTIONS OF SINGULAR AND DEGENERATE PDE'S IN POSSIBLY UNBOUNDED DOMAINS WITH NONNEGATIVE MEAN CURVATURE
Castellaneta, Diego
Farina, Alberto
Valdinoci, Enrico
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2012, 11 (05) : 1983 - 2003
[6] Overdetermined anisotropic elliptic problems
Cianchi, Andrea
Salani, Paolo
[J]. MATHEMATISCHE ANNALEN, 2009, 345 (04) : 859 - 881
[7] Properties of entire solutions of non-uniformly elliptic equations arising in geometry and in phase transitions
Danielli, D
Garofalo, N
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2002, 15 (04) : 451 - 491
[8] C1+ALPHA LOCAL REGULARITY OF WEAK SOLUTIONS OF DEGENERATE ELLIPTIC-EQUATIONS
DIBENEDETTO, E
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1983, 7 (08) : 827 - 850
[9] Dobrushin R., 1992, TRANSLATIONS MATH MO, V104
[10] A pointwise gradient estimate in possibly unbounded domains with nonnegative mean curvature
Farina, Alberto
Valdinoci, Enrico
[J]. ADVANCES IN MATHEMATICS, 2010, 225 (05) : 2808 - 2827

← 1 2 →