Poincar\'e Inequalities and Neumann Problems for the Variable Exponent Setting
Analysis of PDEs
2021-08-24 v1
Abstract
We extend the results of [5], where we proved an equivalence between weighted Poincar\'e inequalities and the existence of weak solutions to a family of Neumann problems related to a degenerate -Laplacian. Here we prove a similar equivalence between Poincar\'e inequalities in variable exponent spaces and solutions to a degenerate -Laplacian, a non-linear elliptic equation with nonstandard growth conditions.
Cite
@article{arxiv.2108.09514,
title = {Poincar\'e Inequalities and Neumann Problems for the Variable Exponent Setting},
author = {David Cruz-Uribe and Michael Penrod and Scott Rodney},
journal= {arXiv preprint arXiv:2108.09514},
year = {2021}
}