On the L^p-theory of Anisotropic singular perturbations of elliptic problems

TL;DR

This paper extends the L^2-theory to L^p spaces for anisotropic singular perturbations in elliptic problems, analyzing convergence and rates in cylindrical domains for both linear and nonlinear cases.

Contribution

It introduces an extension of the L^2-theory to L^p spaces (1<p<2) for anisotropic singular perturbations in elliptic problems, including convergence results and rate estimates.

Findings

Convergence in pseudo Sobolev spaces for weak and entropy solutions

Rate of convergence in cylindrical domains

Extension of L^2-theory to L^p spaces (1<p<2)

Abstract

In this article we give an extention of the L^2-theory of anisotropic singular perturbations for elliptic problems. We study a linear and some nonlinear problems involving L^p data (1<p<2). Convergences in pseudo Sobolev spaces are proved for weak and entropy solutions, and rate of convergence is given in cylindrical domains