A priori estimates for some elliptic equations involving the p-Laplacian

被引：15

作者：

Damascelli, Lucio ^{[1
]}

Pardo, Rosa ^{[2
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

[2] Univ Complutense Madrid, Dept Matemat Aplicada, E-28040 Madrid, Spain

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2018年 / 41卷

关键词：

A priori estimates; Quasilinear elliptic equations with p-Laplacian; Critical Sobolev exponent; Moving planes method; Pohozaev identity; Picone identity; STRONG MAXIMUM PRINCIPLE; POSITIVE SOLUTIONS; WEAK SOLUTIONS; REGULARITY; MONOTONICITY; EXISTENCE; SYMMETRY; THEOREMS; GRADIENT; EIGENVALUE;

D O I：

10.1016/j.nonrwa.2017.11.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Dirichlet problem for positive solutions of the equation -Delta(p)(u) = f(u) in a convex, bounded, smooth domain Omega subset of R-N, with f locally Lipschitz continuous. We provide sufficient conditions guaranteeing L-infinity a priori bounds for positive solutions of some elliptic equations involving the p-Laplacian and extend the class of known nonlinearities for which the solutions are L-infinity a priori bounded. As a consequence we prove the existence of positive solutions in convex bounded domains. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：475 / 496

页数：22

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