English

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}
}