Stable solutions of semilinear elliptic problems in convex domains

DOI10.1007/s000290050022zbMath0905.35032OpenAlexW2077723574MaRDI QIDQ1130213

Xavier Cabré, Sagun Chanillo

Publication date: 20 August 1998

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s000290050022

zbMATH Keywords

critical pointpositive classical solutionslevel curvessemi-stable solution

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Stability in context of PDEs (35B35) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (24)

Some Results for the Gelfand's Problem ⋮ On the number of critical points of solutions of semilinear equations in ℝ2 ⋮ On the number of critical points of the second eigenfunction of the Laplacian in convex planar domains ⋮ Dynamics of non-expansive maps on strictly convex Banach spaces ⋮ Critical points of solutions to a kind of linear elliptic equations in multiply connected domains ⋮ Critical points of solutions to a quasilinear elliptic equation with nonhomogeneous Dirichlet boundary conditions ⋮ On the number of critical points of stable solutions in bounded strip-like domains ⋮ On stationary solutions of two-dimensional Euler equation ⋮ Critical points of positive solutions of nonlinear elliptic equations: multiplicity, location, and non-degeneracy ⋮ Critical points of solutions to quasilinear elliptic problems ⋮ Geometric properties of superlevel sets of semilinear elliptic equations in convex domains ⋮ Uniqueness of the critical point for semi-stable solutions in \(\mathbb{R}^2\) ⋮ Non-existence of patterns and gradient estimates in semilinear elliptic equations with Neumann boundary conditions ⋮ The spectral gap to torsion problem for some non-convex domains ⋮ Parabolic approach to nonlinear elliptic eigenvalue problems ⋮ Nonexistence of multi-bubble solutions to some elliptic equations on convex domains ⋮ Critical points of symmetric solutions to planar quasilinear elliptic problems ⋮ On the number of critical points of solutions of semilinear elliptic equations ⋮ A Morse lemma for degenerate critical points of solutions of nonlinear equations in \(\mathbb{R}^2\) ⋮ Uniqueness of critical points of solutions to the mean curvature equation with Neumann and Robin boundary conditions ⋮ Extremality conditions for the quasi-concavity function and applications ⋮ Critical points of solutions for the mean curvature equation in strictly convex and nonconvex domains ⋮ Geometric properties of the Gelfand problem through a parabolic approach ⋮ Some properties of minimizers of a variational problem involving the total variation functional

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