Dirichlet problem for semilinear edge-degenerate elliptic equations with singular potential term

DOI10.1016/j.jde.2012.01.011zbMath1239.58012OpenAlexW2058268918MaRDI QIDQ765946

Xiaochun Liu, Yawei Wei, Hua Chen

Publication date: 22 March 2012

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2012.01.011

zbMATH Keywords

Poincaré inequalityDirichlet boundary value problemSobolev inequalitysingular potentialmanifolds with edge singularitiesedge Hardy inequality

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61)

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Cites Work

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• Existence theorem for a class of semilinear totally characteristic elliptic equations with critical cone Sobolev exponents
• Cone Sobolev inequality and Dirichlet problem for nonlinear elliptic equations on a manifold with conical singularities
• Pseudo-differential operators, singularities, applications
• Semi-linear sub-elliptic equations on the Heisenberg group with a singular potential
• Dual variational methods in critical point theory and applications
• Elliptic theory of differential edge operators I
• Sobolev met Poincaré
• Ellipticity and invertibility in the cone algebra on \(L_p\)-Sobolev spaces

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