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arXiv · 1704.06376

Optimal domain spaces in Orlicz-Sobolev embeddings

Andrea Cianchi·Vít Musil
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Abstract

We deal with Orlicz-Sobolev embeddings in open subsets of $\mathbb{R}^n$. A necessary and sufficient condition is established for the existence of an optimal, i.e. largest possible, Orlicz-Sobolev space continuously embedded into a given Orlicz space. Moreover, the optimal Orlicz-Sobolev space is exhibited whenever it exists. Parallel questions are addressed for Orlicz-Sobolev embeddings into Orlicz spaces with respect to a Frostman measure, and, in particular, for trace embeddings on the boundary.

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BibTeXRIS

Andrea Cianchi, Vít Musil. 2017-04-21. Optimal domain spaces in Orlicz-Sobolev embeddings. https://doi.org/10.1512/iumj.2019.68.7649

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