Existence and approximation of solutions for a class of degenerate elliptic equations with Neumann boundary condition

Authors

  • Albo Carlos Cavalheiro

DOI:

https://doi.org/10.1285/i15900932v40n2p63

Keywords:

Neumann problem, weighted Sobolev spaces

Abstract

In this work we study the equation $Lu=f$, where $L$ is a degenerate elliptic operator, with Neumann boundary condition in a bounded open set ${\Omega}$. We prove the existence and uniqueness of weak solutions in the weighted Sobolev space ${\mathrm{W}}^{1,2}(\Omega , \omega)$ for the Neumann problem. The main result establishes that a weak solution of degenerate elliptic equations can be approximated by a sequence of solutions for non-degenerate elliptic equations

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Published

17-02-2021

Issue

Volume 40, Issue 2 (2020)

Section

Articoli

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