Elliptic systems in Orlicz-Sobolev spaces with critical sources in bounded domains

Pablo Ochoa

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arXiv · 2503.14667

Elliptic systems in Orlicz-Sobolev spaces with critical sources in bounded domains

Pablo Ochoa

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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.

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Pablo Ochoa. 2025-03-18. Elliptic systems in Orlicz-Sobolev spaces with critical sources in bounded domains. https://arxiv.org/abs/2503.14667

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