Sharp Sobolev inequalities in critical dimensions.

DOI10.1307/mmj/1049832891zbMath1195.35132OpenAlexW2030568535MaRDI QIDQ1396341

Yuxin Ge

Publication date: 30 June 2003

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1307/mmj/1049832891

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Critical exponents in context of PDEs (35B33) Nonlinear elliptic equations (35J60) Variational methods for higher-order elliptic equations (35J35)

Related Items

Remainder terms in a higher order Sobolev inequality, Multiplicity of positive solutions to the boundary-value problems for fractional Laplacians, Adams' inequality and limiting Sobolev embeddings into Zygmund spaces, A critical elliptic problem for polyharmonic operators, Optimal Sobolev and Hardy-Rellich constants under Navier boundary conditions, On fractional Laplacians – 3, Positive solutions in semilinear critical problems for polyharmonic operators, On the Sobolev and Hardy constants for the fractional Navier Laplacian

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The concentration-compactness principle in the calculus of variations. The limit case. II
• Sobolev inequalities with remainder terms
• Symmetry properties in systems of semilinear elliptic equations
• Best constant in Sobolev inequality
• Classification of solutions of higher order conformally invariant equations
• Positive solutions to semilinear polyharmonic Dirichlet problems involving critical Sobolev exponents
• Sobolev spaces on Riemannian manifolds
• Critical exponents and multiple critical dimensions for polyharmonic operators
• Best constant for the embedding of the space \(H^ 2\cap H^ 1_ 0(\Omega)\) into \(L^{2N/(N-4)}\Omega\)
• Critical exponents and critical dimensions of polyharmonic operators
• Critical exponents, critical dimensions and the biharmonic operator
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• The best sobolev constant
• A rellich type identity and applications
• Estimations of the best constant involving the L²norm in Wente's inequality and compact H-surfaces in Euclidean space
• Critical dimensions and higher order Sobolev inequalities with remainder terms