Subcritical approximation of the Sobolev quotient and a related concentration result

DOI10.4171/RSMUP/125-1zbMath1234.35026OpenAlexW2058703908MaRDI QIDQ641032

Giampiero Palatucci

Publication date: 21 October 2011

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/239991

zbMATH Keywords

critical Sobolev exponentconcentration of energy

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Variational methods applied to PDEs (35A15) Critical exponents in context of PDEs (35B33) Variational methods for second-order elliptic equations (35J20)

Related Items

A gamma convergence approach to the critical Sobolev embedding in variable exponent spaces ⋮ Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
• The concentration-compactness principle in the calculus of variations. The limit case. I
• Proof of two conjectures of H. Brezis and L. A. Peletier
• Concentration of low energy extremals
• An introduction to \(\Gamma\)-convergence
• Boundary blow-up for Brezis-Peletier problem on a singular domain
• Concentration of low energy extremals: Identification of concentration points
• Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
• Remarks on some quasilinear elliptic equations