On a new fractional Sobolev space and applications to nonlocal variational problems with variable exponent

By Anouar Bahrouni, Vicentiu D. Rădulescu. 2017

213 citations recorded by the source corpus.

The content of this paper is at the interplay between function spaces $L^{p(x)}$ and $W^{k, p(x)}$ with variable exponents and fractional Sobolev spaces $W^{s, p}$. We are concerned with some qualitative properties of the fractional Sobolev space $W^{s, q(x), p(x, y)}$, where $q$ and $p$ are variable exponents and $s∈ (0, 1)$. We also study a related nonlocal operator, which is a fractional version of the nonhomogeneous $p(x)$-Laplace operator. The abstract results established in this paper are applied in the variational analysis of a class of nonlocal fractional problems with several variable exponents.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/a7433ca3ebbee7f1c79e2a05abda5a9d35e598b8

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In Applied Mathematics

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2. Yun-Ho Kim
3. Patrick Winkert

Citations in the corpus

• A-priori bounds and multiplicity of solutions for nonlinear elliptic problems involving the fractionalp(⋅)-Laplacian (2018, methodology): “( [3]) The operator Φ′ is a mapping of type (S+), i.”