Some critical quasilinear elliptic problems with mixed Dirichlet-Neumann boundary conditions: relation with Sobolev and Hardy-Sobolev optimal constants

DOI10.1016/j.jmaa.2006.11.003zbMath1166.35020OpenAlexW2091479336MaRDI QIDQ884362

Boumediene Abdellaoui, Ireneo Peral Alonso, Eduardo Colorado

Publication date: 6 June 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.11.003

zbMATH Keywords

mixed boundary conditionscritical problems\(p\)-Laplacian like equationsoptimal constants for Hardy-Sobolev inequalities

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Critical exponents in context of PDEs (35B33) Variational methods for second-order elliptic equations (35J20)

Related Items (4)

Some qualitative questions on the equation \(-\operatorname{div}(a(x,u,u))=f(x,u)\) ⋮ Bounds for Sobolev Embedding Constants in Non-simply Connected Planar Domains ⋮ Multiple solutions for weighted nonlinear elliptic system involving critical exponents ⋮ On a Sobolev-type inequality related to the weighted \(p\)-Laplace operator

Cites Work

• The concentration-compactness principle in the calculus of variations. The limit case. II
• Effect of the boundary conditions in the behavior of the optimal constant of some Caffarelli-Kohn-Nirenberg inequalities. Application to some doubly critical nonlinear elliptic problems
• Best constant in weighted Sobolev inequality with weights being powers of distance from the origin
• Semilinear elliptic problems with mixed Dirichlet-Neumann boundary conditions.
• On positive entire solutions to a class of equations with a singular coefficient and critical exponent
• Existence and nonexistence results for a class of parabolic equations with mixed boundary conditions
• Existence and nonexistence results for quasilinear elliptic equations involving the \(p\)-Laplacian with a critical potential
• Some improved Caffarelli-Kohn-Nirenberg inequalities
• Some Remarks on Elliptic Equations with Singular Potentials and Mixed Boundary Conditions
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