Compact embedding theorems and a Lions' type Lemma for fractional\n Orlicz-Sobolev spaces

2020/10/20 by Edcarlos D. Silva, Marcos L. M. Carvalho, Silva, Edcarlos D. +5 · 2 citations
Mathematics · #35A01 #35A02 #35A15 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2010.10277

openalex publication_date 2020/10/20 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

In this paper we are concerned with some abstract results regarding to\nfractional Orlicz-Sobolev spaces. Precisely, we ensure the compactness\nembedding for the weighted fractional Orlicz-Sobolev space into the Orlicz\nspaces, provided the weight is unbounded. We also obtain a version of Lions'\n"vanishing" Lemma for fractional Orlicz-Sobolev spaces, by introducing new\ntechniques to overcome the lack of a suitable interpolation law. Finally, as a\nproduct of the abstract results, we use a minimization method over the Nehari\nmanifold to prove the existence of ground state solutions for a class of\nnonlinear Schr "odinger equations, taking into account unbounded or bounded\npotentials.\n

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• Superlinear fractional Φ-Laplacian type problems via the nonlinear Rayleigh quotient with two parameters
• Fractional Orlicz-Sobolev embeddings into Campanato type spaces

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