The Convexity Estimates for the Solutions of Two Elliptic Equations

DOI10.1080/03605302.2012.727129zbMath1262.35029OpenAlexW2116342599MaRDI QIDQ4902761

Xi-Nan Ma, Yu Ye, Shujun Shi

Publication date: 17 January 2013

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605302.2012.727129

zbMATH Keywords

convex domaintorsion problemcurvature of the boundaryfirst eigenvalue problemcurvature of the solution surface

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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)

Related Items (12)

On concavity of solutions of the nonlinear Poisson equation ⋮ Overdetermined problems for Weingarten hypersurfaces ⋮ Gaussian curvature estimates for the convex level sets of minimal graphs revisited ⋮ Power convexity of a class of elliptic equations involving the Hessian operator in a 3-dimensional bounded convex domain ⋮ Remarks on convexity estimates for solutions of the torsion problem ⋮ Power convexity of solutions to a special Lagrangian equation in dimension two ⋮ Superharmonic functions related to convexity estimates for a class of semilinear elliptic problems ⋮ Convexity estimates for Green's function and the first eigenfunction of Laplace operator ⋮ Superharmonicity of curvature function for the convex level sets of harmonic functions ⋮ Towards optimal gradient bounds for the torsion function in the plane ⋮ Convexity estimates for the solutions of a class of semi-linear elliptic equations ⋮ Convexity estimates for the Green's function

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