On the behaviour of the solutions to p-laplacian equations as p goes to 1

被引：40

作者：

Mercaldo, A. ^{[1
]}

Segura de Leon, S. ^{[2
]}

Trombetti, C. ^{[1
]}

机构：

[1] Univ Naples Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, I-80126 Naples, Italy

[2] Univ Valencia, Dept Anal Matemat, E-46100 Valencia, Spain

来源：

PUBLICACIONS MATEMATIQUES | 2008年 / 52卷 / 02期

关键词：

nonlinear elliptic equations; 1-Laplace operator;

D O I：

10.5565/PUBLMAT_52208_07

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper we study the behaviour as p goes to I of the weak solutions to the problems [GRAPHICS] where Omega is a bounded open set of R-N (N >= 2) with Lipschitz boundary and p > 1. As far as the datum f is concerned, we analyze several cases: the most general one is f epsilon W--1,W-infinity(Omega). We also illustrate our results by means of remarks and examples.

引用

页码：377 / 411

页数：35

共 24 条

[1]

ALVINO A, 1980, RIC MAT, V29, P193

[2]

Ambrosio L., 2000, OXFORD MATH MONOGRAP

[3] The minimizing total variation flow with measure initial conditions [J].