Compactness results for divergence type nonlinear elliptic equations

DOI10.1007/s10231-009-0095-8zbMath1197.35103OpenAlexW2012397978MaRDI QIDQ842514

Marcos Montenegro, Jurandir Ceccon

Publication date: 25 September 2009

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-009-0095-8

zbMATH Keywords

critical Sobolev exponentscompactness of solutionsdivergence type equations

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Second-order elliptic equations (35J15) Elliptic equations on manifolds, general theory (58J05) Variational methods for second-order elliptic equations (35J20)

Related Items

On the compactness problem of extremal functions to sharp Riemannian \(L^p\)-Sobolev inequalities

Cites Work

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• Asymptotic estimates and blow-up theory for critical equations involving the \(p\)-Laplacian
• A compactness theorem for the Yamabe problem
• Conformal deformation of a Riemannian metric to constant scalar curvature
• Regularity for a more general class of quasilinear equations
• Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
• Best constant in Sobolev inequality
• Problèmes isoperimetriques et espaces de Sobolev
• Extremal functions for an optimal Sobolev inequality in the conformal class of the sphere
• Optimal Sobolev inequalities of arbitrary order on compact Riemannian manifolds
• The best constants problem in Sobolev inequalities
• On the best Sobolev inequality
• The strong maximum principle revisited.
• Nonnegative solutions of an elliptic equation and Harnack ends of Riemannian manifolds
• Hölder continuity for solutions of linear degenerate elliptic equations under minimal assumptions
• Geometric inequalities via a general comparison principle for interacting gases
• Best constants in the Sobolev imbedding theorem
• A priori estimates for the Yamabe problem in the non-locally conformally flat case
• Regularity for quasilinear degenerate elliptic equations
• Compactness of solutions to the Yamabe problem. II
• Unique continuation for non-negative solutions of quasilinear elliptic equations
• Sharp Sobolev inequalities with lower order remainder terms
• The 𝐴𝐵 program in geometric analysis: sharp Sobolev inequalities and related problems
• Elliptic equations of Yamabe type
• General optimal euclidean Sobolev and Gagliardo-Nirenberg inequalities
• Homogeneous sharp Sobolev inequalities on product manifolds
• Extremal functions for optimal Sobolev inequalities on compact manifolds
• From best constants to critical functions