A natural approach to the asymptotic mean value property for the \(p\)-Laplacian

DOI10.1007/s00526-017-1188-7zbMath1378.35147arXiv1604.00520OpenAlexW2964086475MaRDI QIDQ2406061

Rolando Magnanini, Michinori Ishiwata, Hidemitsu Wadade

Publication date: 26 September 2017

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.00520

zbMATH Keywords

viscosity solutionparabolic \(p\)-Laplace equationasymptotic mean value propertynormalized elliptic \(p\)-Laplace equation

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Quasilinear parabolic equations with (p)-Laplacian (35K92) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (14)

Convergence of natural \(p\)-means for the \(p\)-Laplacian in the Heisenberg group ⋮ An asymptotic expansion for the fractional p-Laplacian and for gradient-dependent nonlocal operators ⋮ Nearly optimal stability for Serrin's problem and the soap bubble theorem ⋮ Short-time behavior for game-theoretic \(p\)-caloric functions ⋮ Variational approach to the asymptotic mean-value property for the \(p\)-Laplacian on Carnot groups ⋮ A game theoretical approximation for a parabolic/elliptic system with different operators ⋮ Asymptotic average solutions to linear second order semi-elliptic PDEs: a Pizzetti-type theorem ⋮ A game theoretical approximation for solutions to nonlinear systems with obstacle-type equations ⋮ Boundary convergence properties of \(L^p\)-averages ⋮ A game theoretical approach for a nonlinear system driven by elliptic operators ⋮ A mean value formula for the variational \(p\)-Laplacian ⋮ Variational \(p\)-harmonious functions: existence and convergence to \(p\)-harmonic functions ⋮ Asymptotics for the resolvent equation associated to the game-theoretic p-laplacian ⋮ Convergence of the naturalp-means for thep-Laplacian

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