On concavity of solutions of the Dirichlet problem for the equation \((-\Delta)^{1/2} \varphi = 1\) in convex planar regions

DOI10.4171/JEMS/695zbMath1365.35211arXiv1405.3846MaRDI QIDQ2628336

Tadeusz Kulczycki

Publication date: 1 June 2017

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.3846

zbMATH Keywords

concavityharmonic functionCauchy processHessian matrixfractional Laplacianfirst exit time

Mathematics Subject Classification ID

Boundary value problems for PDEs with pseudodifferential operators (35S15) Convexity properties of solutions to PDEs with constant coefficients (35E10) Fractional partial differential equations (35R11) Topological and monotonicity methods applied to PDEs (35A16)

Related Items (7)

Power- and log-concavity of viscosity solutions to some elliptic Dirichlet problems ⋮ Existence and convexity of solutions of the fractional heat equation ⋮ Gaussian curvature estimates for the convex level sets of minimal graphs revisited ⋮ Power convexity of solutions to a special Lagrangian equation in dimension two ⋮ Universal constraints on the location of extrema of eigenfunctions of non-local Schrödinger operators ⋮ On the first eigenfunction of the symmetric stable process in a bounded Lipschitz domain ⋮ Superharmonicity of curvature function for the convex level sets of harmonic functions

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