Games for eigenvalues of the Hessian and concave/convex envelopes

DOI10.1016/j.matpur.2018.08.007zbMath1423.35118arXiv1801.03383OpenAlexW2963433336MaRDI QIDQ2317076

Pablo Blanc, Julio D. Rossi

Publication date: 8 August 2019

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.03383

zbMATH Keywords

eigenvalues of the Hessiangamesconcave/convex envelopes

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Convexity of real functions of several variables, generalizations (26B25) Viscosity solutions to PDEs (35D40)

Related Items (32)

Asymptotic mean-value formulas for solutions of general second-order elliptic equations ⋮ Fractional truncated Laplacians: representation formula, fundamental solutions and applications ⋮ A regularity result for a class of non-uniformly elliptic operators ⋮ Asymptotic mean value formulas for parabolic nonlinear equations ⋮ Reverse Faber-Krahn inequality for a truncated Laplacian operator ⋮ Fractional convexity ⋮ Existence issues for a large class of degenerate elliptic equations with nonlinear Hamiltonians ⋮ Singular elliptic equations with directional diffusion ⋮ Existence through convexity for the truncated Laplacians ⋮ Unnamed Item ⋮ An asymptotic mean value formula for eigenvalues of the Hessian related to concave/convex envelopes ⋮ Asymptotic \(C^{1,\gamma}\)-regularity for value functions to uniformly elliptic dynamic programming principles ⋮ A game theoretical approximation for a parabolic/elliptic system with different operators ⋮ Game-theoretic approach to Hölder regularity for PDEs involving eigenvalues of the Hessian ⋮ A Vázquez-type strong minimum/maximum principle for partial trace operators ⋮ Viscosity solutions to complex first eigenvalue equations ⋮ A game theoretical approximation for solutions to nonlinear systems with obstacle-type equations ⋮ Characterizations of the viscosity solution of a nonlocal and nonlinear equation induced by the fractional \(p\)-Laplace and the fractional \(p\)-convexity ⋮ Games associated with products of eigenvalues of the Hessian ⋮ Unnamed Item ⋮ A game theoretical approach for a nonlinear system driven by elliptic operators ⋮ The Inverse Problem for Hamilton--Jacobi Equations and Semiconcave Envelopes ⋮ Positivity sets of supersolutions of degenerate elliptic equations and the strong maximum principle ⋮ Maximum principles for viscosity solutions of weakly elliptic equations ⋮ Convex envelopes on Trees ⋮ Regularity properties for a class of non-uniformly elliptic Isaacs operators ⋮ The evolution problem associated with eigenvalues of the Hessian ⋮ Evolution equations involving nonlinear truncated Laplacian operators ⋮ Convex and quasiconvex functions in metric graphs ⋮ Towards a reversed Faber-Krahn inequality for the truncated Laplacian ⋮ Local regularity estimates for general discrete dynamic programming equations ⋮ Lipschitz estimates for partial trace operators with extremal Hessian eigenvalues

Cites Work

• Unnamed Item
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• The convex envelope is the solution of a nonlinear obstacle problem
• On the mean value property for the $p$-Laplace equation in the plane
• An asymptotic mean value characterization for 𝑝-harmonic functions
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• User’s guide to viscosity solutions of second order partial differential equations
• p-convexity, p-plurisubharmonicity, and the Levi problem

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