The double phase Dirichlet problem when the lowest exponent is equal to 1
Analysis of PDEs
2023-04-06 v1 Functional Analysis
Abstract
In this paper we prove an existence and uniqueness result for the double phase Dirichlet problem when the lowest exponent is equal to 1. Our solution is a function of bounded variation that simultaneously lies in a suitable weighted Sobolev space and is found as the limit of a sequence of solutions of intermediate double phase Dirichlet problems whose lowest exponent goes to 1. As a result of that, our approach involves the study of some relevant properties of generalized Orlicz-Sobolev spaces.
Cite
@article{arxiv.2301.08119,
title = {The double phase Dirichlet problem when the lowest exponent is equal to 1},
author = {Alexandros Matsoukas and Nikos Yannakakis},
journal= {arXiv preprint arXiv:2301.08119},
year = {2023}
}