The power concavity of solutions of some semilinear elliptic boundary-value problems

DOI10.1017/S0004972700004676zbMath0554.35047MaRDI QIDQ3216971

G. Keady

Publication date: 1985

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

power concavitysemilinear elliptic boundary-value problems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (4)

On concavity of solutions of the nonlinear Poisson equation ⋮ Concavity of solutions to semilinear equations in dimension two ⋮ Geometric properties of superlevel sets of semilinear elliptic equations in convex domains ⋮ A Hadamard-jensen inequality and an application to the elastic torsion problem

Cites Work

• Maximum principles and their applications
• On the convexity of level lines of the fundamental mode in the clamped membrane problem, and the existence of convex solutions in a related free boundary problem
• Solution of Dirichlet's problem for the equation \(\Delta u = -1\) in a convex region
• Convexity properties of solutions to some classical variational problems
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