Optimal Sobolev inequalities and extremal functions. The three dimensional case

DOI10.1512/iumj.2002.51.2111zbMath1037.58012OpenAlexW1998235916MaRDI QIDQ4545175

Olivier Druet

Publication date: 14 August 2002

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1512/iumj.2002.51.2111

zbMATH Keywords

extremal functionscompact manifoldsSobolev inequalities

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Elliptic equations on manifolds, general theory (58J05) Variational methods for second-order elliptic equations (35J20)

Related Items (15)

Sobolev inequalities for the Hardy-Schrödinger operator: extremals and critical dimensions ⋮ The second best constant for the Hardy-Sobolev inequality on manifolds ⋮ Hardy-singular boundary mass and Sobolev-critical variational problems ⋮ The Hardy-Schrödinger operator with interior singularity: the remaining cases ⋮ On solutions for strongly coupled critical elliptic systems on compact Riemannian manifolds ⋮ Hardy-Sobolev equations on compact Riemannian manifolds ⋮ On some conjectures proposed by Haïm Brezis. ⋮ From best constants to critical functions ⋮ Existence and regularity of maximal metrics for the first Laplace eigenvalue on surfaces ⋮ Hardy-Sobolev inequality with higher dimensional singularity ⋮ Sharp Sobolev inequalities in the presence of a twist ⋮ Elliptic equations in dimension three: A conjecture of H. Brezis ⋮ On a rigidity result for the first conformal eigenvalue of the Laplacian ⋮ Elliptic equations with critical Sobolev exponents in dimension 3 ⋮ The Hardy-Schrödinger operator on the Poincaré ball: compactness, multiplicity, and stability of the Pohozaev obstruction

This page was built for publication: Optimal Sobolev inequalities and extremal functions. The three dimensional case