Optimal Sobolev inequalities of arbitrary order on compact Riemannian manifolds

DOI10.1006/jfan.1998.3264zbMath0923.46035OpenAlexW2012772119MaRDI QIDQ1273949

Olivier Druet

Publication date: 15 October 1999

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1998.3264

zbMATH Keywords

scalar curvatureoptimal Sobolev inequalitysmooth compact \(n\)-dimensional Riemannian manifold

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Elliptic equations on manifolds, general theory (58J05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

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• The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds
• Best constants in the Sobolev imbedding theorem
• On some nonlinear equations involving the \(p\)-Laplacian with critical Sobolev growth
• Local behavior of solutions of quasi-linear equations
• A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
• On harnack type inequalities and their application to quasilinear elliptic equations

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