Weighted p--Laplace approximation of linear and quasi-linear elliptic problems with measure data

Autor:	Eymard, Robert, Maltese, David, Prignet, Alain
Rok vydání:	2022
Předmět:	Mathematics - Classical Analysis and ODEs
Druh dokumentu:	Working Paper
Popis:	We approximate the solution to some linear and degenerate quasi-linear problem involving a linear elliptic operator (like the semi-discrete in time implicit Euler approximation of Richards and Stefan equations) with measure right-hand side and heterogeneous anisotropic diffusion matrix. This approximation is obtained through the addition of a weighted p--Laplace term. A well chosen diffeomorphism between R and (--1, 1) is used for the estimates of the approximated solution, and is involved in the above weight. We show that this approximation converges to a weak sense of the problem for general right-hand-side, and to the entropy solution in the case where the right-hand-side is in L 1 .
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2205.07698 Zobrazit plný text záznamu View this record from Arxiv