On the Aleksandrov-Bakel'man-Pucci Estimate for Some Elliptic and Parabolic Nonlinear Operators

被引：13

作者：

Argiolas, Roberto ^{[1
]}

Charro, Fernando ^{[1
]}

Peral, Ireneo ^{[1
,2
]}

机构：

[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[2] ICMAT, Madrid 28049, Spain

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2011年 / 202卷 / 03期

关键词：

VISCOSITY SOLUTIONS; DIRICHLET PROBLEM; MAXIMUM PRINCIPLE; EQUATIONS; INEQUALITY; UNIQUENESS;

D O I：

10.1007/s00205-011-0434-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we prove the Aleksandrov-Bakel'man-Pucci estimate for (possibly degenerate) nonlinear elliptic and parabolic equations of the form -div (F (del u(x))) = f(x) in Omega subset of R-n and u(t) (x, t) - div ((F (del u(x, t))) = f (x, t) in Q subset of Rn+1 for F a C-1 monotone field under some suitable conditions. Examples of applications such as the p-Laplacian and the Mean Curvature Flow are considered, as well as extensions of the general results to equations that are not in divergence form, such as the m-curvature flow.

引用

页码：875 / 917

页数：43

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