Elliptic systems in Orlicz-Sobolev spaces with critical sources in bounded domains
Analysis of PDEs
2025-03-20 v1
Abstract
In this paper, we show the existence of non-trivial solutions to very general elliptic systems with critical non-linearities in the sense of embeddings in Orlicz-Sobolev spaces. This allows to consider non-linearities which do not have polynomial growth. To achieve the existence, we combine a Mountain Pass Theorem without the Palais-Smale condition with the second Concentration Compactness Principle of Lions in Orlicz-Sobolev spaces.
Keywords
Cite
@article{arxiv.2503.14667,
title = {Elliptic systems in Orlicz-Sobolev spaces with critical sources in bounded domains},
author = {Pablo Ochoa},
journal= {arXiv preprint arXiv:2503.14667},
year = {2025}
}