Fractional Sobolev spaces with variable exponents and fractional p(x)-Laplacians

By U. Kaufmann, Julio D. Rossi, R. Vidal. 2017

194 citations recorded by the source corpus.

In this article we extend the Sobolev spaces with variable exponents to include the fractional case, and we prove a compact embedding theorem of these spaces into variable exponent Lebesgue spaces. As an application we prove the existence and uniqueness of a solution for a nonlocal problem involving the fractional p(x)-Laplacian.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/995f9e03c16d2dffdad7a1639fa6a16940b9153e

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In Applied Mathematics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

A-priori bounds and multiplicity of solutions for nonlinear elliptic problems involving the fractionalp(⋅)-Laplacian (2018, methodology): “h spaces have not been well-deﬁned as well as not many properties on such spaces have been established. In this paper we ﬁrst reﬁne the fractional Sobolev space with variable exponent investigated in [2,3,11] and obtain fundamental imbeddings on our space. With these imbeddings in hand, we investiga”
Basic results of fractional Orlicz-Sobolev space and applications to non-local problems (2019, background): “tions involving the fractional p(x)−Laplace operator. In fact, results for the fractional Sobolev spaces with variable exponent and fractional p(x)−Laplace equations are few, for example, we refer to [5, 6, 24, 38]. In the theory of PDEs, when trying to relax some conditions on the operators, such a”
Traces for fractional Sobolev spaces with variable exponents (2017, background): “th the norm kfks,p(·,·) := kfkLp¯(·)(Ω) +[f]s,p(·,·). To show this fact, one just has to follow the arguments in [5] for the constant exponent case. This space Ws,p(·,·)(Ω) was recently introduced in [8]. For general theory of classical Sobolev spaces we refer the reader to [1, 3] and for the variab”