Fractional Sobolev spaces with variable exponents and fractional p(X)-Laplacians
TLDR
Kaufmann et al. as discussed by the authors presented the work of the Centro de Investigacion y Estudios de Matematica (CESM) at the Universidad Nacional de Cordoba.Abstract:
Fil: Kaufmann, Uriel. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Cordoba. Centro de Investigacion y Estudios de Matematica. Universidad Nacional de Cordoba. Centro de Investigacion y Estudios de Matematica; Argentinaread more
Citations
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On a new fractional Sobolev space and applications to nonlocal variational problems with variable exponent
TL;DR: In this article, a variational analysis of a class of nonlocal fractional problems with variable exponents was performed in the context of non-homogeneous Laplace operators, and the abstract results established in this paper are applied in the variational analyses of a related non-local operator, which is a fractional version of the nonhomogeneous $p(x)$-Laplace operator.
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Multiplicity results for variable-order fractional Laplacian equations with variable growth
TL;DR: In this paper, the multiplicity of solutions for an elliptic type problem driven by the variable-order fractional Laplace operator involving variable exponents was studied, and it was shown that these two solutions converge to two solutions of a limit problem as λ → ∞.
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Eigenvalue problems involving the fractional $p(x)$-Laplacian operator
TL;DR: In this article, the existence of a continuous family of eigenvalues lying in a neighborhood at the right of the origin was established using Ekeland's variational principle, based on a variational approach.
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A-priori bounds and multiplicity of solutions for nonlinear elliptic problems involving the fractional p(⋅)-Laplacian
Ky Ho,Yun-Ho Kim +1 more
TL;DR: In this paper, the authors obtained fundamental imbeddings for fractional Sobolev spaces with variable exponents, which are a generalization of the well-known FSM spaces.
Traces for fractional Sobolev spaces with variable exponents
TL;DR: In this article, a trace theorem in fractional spaces with variable exponents was proved for the case of lebesgue norms with variable exponent, and the inequality was shown to hold.
References
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Hitchhiker's guide to the fractional Sobolev spaces
TL;DR: In this article, the authors deal with the fractional Sobolev spaces W s;p and analyze the relations among some of their possible denitions and their role in the trace theory.
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Lebesgue and Sobolev Spaces with Variable Exponents
TL;DR: In this paper, a framework for function spaces is presented, which includes variable exponent Lebesgue spaces, the maximal operator, the generalized Muckenhoupt condition, and transfer techniques.
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Functional Spaces for the Theory of Elliptic Partial Differential Equations
Abstract: Preliminaries on ellipticity.- Notions from Topology and Functional Analysis.- Sobolev Spaces and Embedding Theorems.- Traces of Functions on Sobolev Spaces.- Fractional Sobolev Spaces.- Elliptic PDE: Variational Techniques.- Distributions with measures as derivatives.- Korn's Inequality in Lp.- Appendix on Regularity.
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Overview of differential equations with non-standard growth
TL;DR: An overview of the field of differential equations with non-standard growth, which considers both existence and regularity questions, as well as several of the most important results.
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Local behavior of fractional p-minimizers
TL;DR: In this paper, the De Giorgi-Nash-Moser theory was extended to nonlocal, possibly degenerate integro-differential operators, and they extended it to non-local integro differential operators.