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Fractional variable exponents Sobolev trace spaces and Dirichlet problem for the regional fractional p(.) -Laplacian

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Abstract

In this paper we give a finer analysis of fractional variable exponents Sobolev spaces. We use the relative capacity to characterize completely the zero trace fractional variable exponents Sobolev spaces. We also give a relative capacity criterium for removable sets. As an application we study the Dirichlet problem for the regional fractional p(.)-Laplacian.

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  1. Laboratory of Partial Differential Equations, Algebra and Spectral Geometry, Higher School of Education and Training, Ibn Tofail University, P.O.Box 242-Kenitra 14000, Kenitra, Morocco

    Mohamed Berghout

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  1. Mohamed Berghout
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Berghout, M. Fractional variable exponents Sobolev trace spaces and Dirichlet problem for the regional fractional p(.) -Laplacian. J Elliptic Parabol Equ 9, 565–594 (2023). https://doi.org/10.1007/s41808-023-00213-z

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