On the Sobolev trace Theorem for variable exponent spaces in the critical range

2013/01/14 by Julián Fernández Bonder, Bonder, Julian Fernandez, Nicolas Saintier +3
Mathematics · #35B33 #46E35 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1301.2961

openalex publication_date 2013/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the Sobolev Trace Theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. Then we give local conditions on the exponents and on the domain (in the spirit of Adimurthy and Yadava) in order to satisfy such conditions, and therefore to ensure the existence of extremals.

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