Elliptic equations with critical growth and a large set of boundary singularities

DOI10.1090/S0002-9947-09-04655-8zbMath1187.35085arXivmath/0508348MaRDI QIDQ3394978

Nassif Ghoussoub, Frédéric Robert

Publication date: 11 September 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0508348

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61)

Related Items (10)

Sobolev inequalities for the Hardy-Schrödinger operator: extremals and critical dimensions ⋮ A note on the sign-changing solutions for a double critical Hardy-Sobolev-Maz'ya problem ⋮ Hardy-Sobolev inequality with singularity a curve ⋮ On the Dirichlet problem generated by the Maz'ya-Sobolev inequality ⋮ Infinitely many solutions for a Hardy-Sobolev equation involving critical growth ⋮ Minimization problem on the Hardy-Sobolev inequality ⋮ A critical problem on the Hardy-Sobolev inequality in boundary singularity case ⋮ Asymptotic behavior of the least-energy solutions of a semilinear elliptic equation with the Hardy-Sobolev critical exponent ⋮ The role of the mean curvature in a Hardy-Sobolev trace inequality ⋮ Hardy-Sobolev inequality with higher dimensional singularity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Sobolev-Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics
• Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
• The effect of curvature on the best constant in the Hardy-Sobolev inequalities
• Elliptic equations with nearly critical growth
• Symmetry and related properties via the maximum principle
• The best constants problem in Sobolev inequalities
• Elliptic equations with critical Sobolev exponents in dimension 3
• Hardy-Sobolev critical elliptic equations with boundary singularities
• Critical functions and optimal Sobolev inequalities
• Asymptotic behaviour of a nonlinear elliptic equation with critical Sobolev exponent: the radial case. II
• The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds
• Prescribed scalar curvature on the \(n\)-sphere
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Concentration estimates for Emden-Fowler equations with boundary singularities and critical growth
• Positive Solutions of Semilinear Equations in Cones
• Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents
• A 𝐶⁰-theory for the blow-up of second order elliptic equations of critical Sobolev growth
• Elliptic equations of Yamabe type
• From best constants to critical functions

This page was built for publication: Elliptic equations with critical growth and a large set of boundary singularities