The behavior of the best Sobolev trace constant and extremals in thin domains.

DOI10.1016/j.jde.2003.07.011zbMath1138.35023OpenAlexW2114975617MaRDI QIDQ1428437

Julián Fernández Bonder, Julio D. Rossi, Sandra R. Martinez

Publication date: 29 March 2004

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2003.07.011

zbMATH Keywords

eigenvalue problems\(p\)-Laplaciannonlinear boundary conditionsSobolev trace constants

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Estimates of eigenvalues in context of PDEs (35P15) Variational methods for second-order elliptic equations (35J20)

Related Items (10)

Multiple solutions of a quasilinear elliptic problem involving nonlinear boundary condition on exterior domain ⋮ Multiplicity results for nonlinear Neumann boundary value problems involving \(p\)-Laplace type operators ⋮ On the best Sobolev trace constant and extremals in domains with holes ⋮ Optimal boundary holes for the Sobolev trace constant ⋮ Sign-changing and extremal constant-sign solutions of nonlinear elliptic Neumann boundary value problems ⋮ A variational approach to a quasilinear elliptic problem involving the \(p\)-Laplacian and nonlinear boundary condition ⋮ AN OPTIMIZATION PROBLEM RELATED TO THE BEST SOBOLEV TRACE CONSTANT IN THIN DOMAINS ⋮ Existence of infinitely many weak solutions for the \(p\)-Laplacian with nonlinear boundary conditions ⋮ Linking solutions for \(p\)-Laplace equations with nonlinear boundary conditions and indefinite weight ⋮ Asymptotics of best Sobolev constants on thin manifolds

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