Basic results of fractional Orlicz-Sobolev space and applications to non-local problems

DOI10.12775/TMNA.2019.111zbMath1448.35242arXiv1901.00784MaRDI QIDQ2194630

Sabri Bahrouni, Hichem Ounaies, Leandro S. Tavares

Publication date: 4 September 2020

Published in: Topological Methods in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.00784

zbMATH Keywords

existence of solutionsfractional Orlicz-Sobolev spacefractional \(M\)-Laplacian

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Fractional partial differential equations (35R11) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (27)

Least-energy nodal solutions of nonlinear equations with fractional Orlicz–Sobolev spaces ⋮ Problems involving the fractional g-Laplacian with lack of compactness ⋮ Fractional N-Laplacian boundary value problems with jumping nonlinearities in the fractional Orlicz-Sobolev spaces ⋮ Interior and up to the boundary regularity for the fractional \(g\)-Laplacian: The convex case ⋮ Embedding and extension results in fractional Musielak–Sobolev spaces ⋮ Multiplicity of solutions for nonlocal parametric elliptic systems in fractional Orlicz-Sobolev spaces ⋮ Sign-changing solution for a generalized Kirchhoff problem in the fractional Orlicz-Sobolev space with nonsmooth nonlinearity ⋮ A note on Hopf's lemma and strong minimum principle for nonlocal equations with non-standard growth ⋮ Variational eigenvalues of the fractional g-Laplacian ⋮ A new class of fractional Orlicz-Sobolev space and singular elliptic problems ⋮ A Moser-Trudinger type inequality on the Orlicz fractional space ⋮ On the L^∞‐regularity for fractional Orlicz problems via Moser's iteration ⋮ Existence and multiplicity of solutions for a Dirichlet problem in fractional Orlicz-Sobolev spaces ⋮ On fractional Musielak-Sobolev spaces and applications to nonlocal problems ⋮ Infinitely many solutions for problems in fractional Orlicz-Sobolev spaces ⋮ Compact embedding theorems and a Lions' type lemma for fractional Orlicz-Sobolev spaces ⋮ On a class of nonvariational problems in fractional Orlicz-Sobolev spaces ⋮ On the limit as \(s\to 1^-\) of possibly non-separable fractional Orlicz-Sobolev spaces ⋮ Embedding theorems in the fractional Orlicz-Sobolev space and applications to non-local problems ⋮ Existence of a solution to a nonlocal Schrödinger system problem in fractional modular spaces ⋮ Hardy and Poincaré inequalities in fractional Orlicz-Sobolev spaces ⋮ Neumann and Robin type boundary conditions in Fractional Orlicz-Sobolev spaces ⋮ Ground state solutions for a nonlocal system in fractional Orlicz-Sobolev spaces ⋮ Regularity for nonlocal problems with non-standard growth ⋮ Ground state and nodal solutions for fractional Orlicz problems with lack of regularity and without the Ambrosetti-Rabinowitz condition ⋮ Existence of solutions to fractional elliptic equation with the Hardy potential and concave-convex nonlinearities ⋮ Maz’ya–Shaposhnikova formula in magnetic fractional Orlicz–Sobolev spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlocal diffusion and applications
• Hitchhiker's guide to the fractional Sobolev spaces
• Lebesgue and Sobolev spaces with variable exponents
• Trudinger-Moser type inequality and existence of solution for perturbed non-local elliptic operators with exponential nonlinearity
• Mountain pass solutions for non-local elliptic operators
• On the isometries of certain function-spaces
• Ground state solutions of scalar field fractional Schrödinger equations
• Neumann problems associated to nonhomogeneous differential operators in Orlicz-Sobolev spaces
• Variational problems with free boundaries for the fractional Laplacian
• On the existence of multiple positive solutions of quasilinear elliptic eigenvalue problems
• On principal eigenvalues for quasilinear elliptic differential operators: an Orlicz-Sobolev space setting
• Mountain pass type solutions for quasilinear elliptic equations
• Electrorheological fluids: modeling and mathematical theory
• Multiplicity results for variable-order fractional Laplacian equations with variable growth
• On a new fractional Sobolev space and applications to nonlocal variational problems with variable exponent
• Comparison and sub-supersolution principles for the fractional \(p(x)\)-Laplacian
• Variational methods for non-local operators of elliptic type
• Fractional order Orlicz-Sobolev spaces
• Elliptic problems involving the fractional Laplacian in \(\mathbb R^N\)
• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
• Fractional Elliptic Problems with Critical Growth in the Whole of ℝn
• Positive Solutions of Quasilinear Elliptic Equations with Critical Orlicz-Sobolev Nonlinearity on RN
• Variational Methods for Nonlocal Fractional Problems
• Soliton Like Solutions of a Lorentz Invariant Equation in Dimension 3
• Fractional Sobolev spaces with variable exponents and fractional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mrow> <mml:mo form="prefix">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo form="postfix">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math>-Laplacians
• The natural generalizationj of the natural conditions of ladyzhenskaya and uralľtseva for elliptic equations
• Partial Differential Equations with Variable Exponents
• An Extension Problem Related to the Fractional Laplacian
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)

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