AN ELLIPTIC NEUMANN PROBLEM WITH CRITICAL NONLINEARITY IN THREE DIMENSIONAL DOMAINS

DOI10.1142/S0219199799000158zbMath0954.35065OpenAlexW2082153970MaRDI QIDQ4514925

Olivier Rey

Publication date: 14 November 2000

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219199799000158

zbMATH Keywords

mean curvature of the domain boundarysolution with low energy

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Critical exponents in context of PDEs (35B33)

Related Items (21)

Locating the peaks of solutions via the maximum principle: I. The Neumann problem ⋮ Blowing up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity. I: \(N=3\) ⋮ Boundary separated and clustered layer positive solutions for an elliptic Neumann problem with large exponent ⋮ Bubble accumulations in an elliptic Neumann problem with critical Sobolev exponent ⋮ Solutions to a nonlinear Neumann problem in three-dimensional exterior domains ⋮ Solutions with clustered bubbles and a boundary layer of an elliptic problem ⋮ Boundary-layers for a Neumann problem at higher critical exponents ⋮ Nonexistence of interior bubbling solutions for slightly supercritical elliptic problems ⋮ Bubbling phenomenon for semilinear Neumann elliptic equations of critical exponential growth ⋮ The question of interior blow-up points for an elliptic Neumann problem: the critical case. ⋮ Infinitely many solutions for an elliptic Neumann problem involving critical Sobolev growth ⋮ Singular radial solutions for the Lin-Ni-Takagi equation ⋮ Arbitrary many boundary peak solutions for an elliptic Neumann problem with critical growth ⋮ Interior bubbling solutions for the critical Lin-Ni-Takagi problem in dimension 3 ⋮ Blowing up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity. II: \(N\geqslant 4\) ⋮ Sign changing bubbling solutions for a critical Neumann problem in 3D ⋮ Super-critical boundary bubbling in a semilinear Neumann problem ⋮ A Neumann problem with critical exponent in nonconvex domains and Lin-Ni’s conjecture ⋮ Solutions with interior bubble and boundary layer for an elliptic Neumann problem with critical nonlinearity ⋮ Curve-Like Concentration Layers for a Singularly Perturbed Nonlinear Problem with Critical Exponents ⋮ Bubbling on boundary submanifolds for a semilinear Neumann problem near high critical exponents

Cites Work

• Interaction between the geometry of the boundary and positive solutions of a semilinear Neumann problem with critical nonlinearity
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents

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