Symmetry and Regularity of Solutions to the Weighted Hardy–Sobolev Type System

DOI10.1515/ans-2015-5005zbMath1382.35326OpenAlexW2471102904MaRDI QIDQ2789492

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Publication date: 1 March 2016

Published in: Advanced Nonlinear Studies (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ans-2015-5005

zbMATH Keywords

regularityHardy-Littlewood-Sobolev inequalityradial symmetrymethod of moving planes in integral forms

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Function spaces arising in harmonic analysis (42B35) Systems of nonlinear integral equations (45G15) Fractional partial differential equations (35R11) Symmetries, invariants, etc. in context of PDEs (35B06)

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Cites Work

• Unnamed Item
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• A Liouville type theorem for poly-harmonic Dirichlet problems in a half space
• Hardy-Littlewood-Sobolev and Stein-Weiss inequalities and integral systems on the Heisenberg group
• Asymptotic radial symmetry and growth estimates of positive solutions to weighted Hardy-Littlewood-Sobolev system of integral equations
• Regularity of solutions for an integral system of Wolff type
• Symmetry and regularity of extremals of an integral equation related to the Hardy-Sobolev inequality
• Liouville-type theorems and decay estimates for solutions to higher order elliptic equations
• Axial symmetry and regularity of solutions to an integral equation in a half-space
• Weighted Hardy-Littlewood-Sobolev inequalities and systems of integral equations
• Results on positive solutions of elliptic equations with a critical Hardy-Sobolev operator
• Classification of solutions of some nonlinear elliptic equations
• Classification of solutions of higher order conformally invariant equations
• The maximum principles and symmetry results for viscosity solutions of fully nonlinear equations
• A symmetry problem in potential theory
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• A Liouville Type Theorem for Poly-harmonic System with Dirichlet Boundary Conditions in a Half Space
• The best constant in a weighted Hardy-Littlewood-Sobolev inequality
• Classification of solutions for an integral equation
• Liouville-type theorems for fully nonlinear elliptic equation in half spaces