Starshapedness of level sets of solutions to elliptic PDEs

DOI10.1080/00036810412331297262zbMath1130.35055OpenAlexW2005156930WikidataQ58277013 ScholiaQ58277013MaRDI QIDQ5713483

Paolo Salani

Publication date: 14 December 2005

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036810412331297262

zbMATH Keywords

elliptic equationsviscosity solutionsstarshaped envelopestarshapedness of level sets

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Variants of convex sets (star-shaped, ((m, n))-convex, etc.) (52A30)

Related Items

Unnamed Item, Strict starshapedness of solutions to the horizontal \(p\)-Laplacian in the Heisenberg group, A two phase free boundary problem related to quadrature domains, Some geometric conjectures in harmonic function theory, Geometric properties of superlevel sets of semilinear elliptic equations in convex domains, The concavity region of solutions to the Poisson equation in the plane, Starshaped sets, Quasi-concavity for semilinear elliptic equations with non-monotone and anisotropic nonlinearities, Starshapedeness for fully non‐linear equations in Carnot groups

Cites Work

• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• Strong maximum principle for semicontinuous viscosity solutions of nonlinear partial differential equations
• On convexity and starshapedness of level sets for some nonlinear elliptic and parabolic problems on convex rings
• Blow-up in exterior domains: existence and star-shapedness
• Existence and starshapedness for the lane-emden equation
• User’s guide to viscosity solutions of second order partial differential equations
• Starshapedness of Level Sets for Solutions of Nonlinear Elliptic Equations
• On the uniqueness, monotonicity, starlikeness, and convexity of solutions for a nonlinear boundary value problem in elliptic PDEs
• Weak solutions of hessian equations
• Quasi–concave envelope of a function and convexity of level sets of solutions to elliptic equations