The Matzoh Ball Soup Problem: A complete characterization

Magnanini, Rolando; Marini, Michele

doi:10.1016/j.na.2015.06.022

Nonlinear Analysis

2016

DOI: 10.1016/j.na.2015.06.022

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The Matzoh Ball Soup Problem: A complete characterization

Rolando Magnanini

Michele Marini

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Cited by 2 publications

References 16 publications

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Short-time behavior for game-theoretic p-caloric functions

Berti

Magnanini

2019

Journal de Mathématiques Pures et Appliquées

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We consider the solution of ut − ∆ G p u = 0 in a (not necessarily bounded) domain, satisfying u = 0 initially and u = 1 on the boundary at all times. Here, ∆ G p u is the game-theoretic or normalized p-laplacian. We derive new precise asymptotic formulas for short times, that generalize the work of S. R. S. Varadhan [Va] for large deviations and that of the second author and S. Sakaguchi [MS1] for the heat content of a ball touching the boundary. We also compute the short-time behavior of the q-mean of u on such a ball. Applications to time-invariant level surfaces of u are then derived.2010 Mathematics Subject Classification. Primary 35K92; Secondary 35K20, 35B40, 35Q91.

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Short-time behavior for game-theoretic p-caloric functions

Berti

Magnanini

2019

Journal de Mathématiques Pures et Appliquées

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Asymptotics for the resolvent equation associated to the game-theoreticp-laplacian

Berti

Magnanini

2018

Applicable Analysis

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We consider the (viscosity) solution u ε of the elliptic equation ε 2 ∆ G p u = u in a domain (not necessarily bounded), satisfying u = 1 on its boundary. Here, ∆ G p is the game-theoretic or normalized p-laplacian. We derive asymptotic formulas for ε → 0 + involving the values of u ε , in the spirit of Varadhan's work [Va], and its q-mean on balls touching the boundary, thus generalizing that obtained in [MS1] for p = q = 2. As in a related parabolic problem, investigated in [BM], we link the relevant asymptotic behavior to the geometry of the domain. 2010 Mathematics Subject Classification. Primary 35J92; Secondary 35J25, 35B40, 35Q91.

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The Matzoh Ball Soup Problem: A complete characterization

Cited by 2 publications

References 16 publications

Short-time behavior for game-theoretic p-caloric functions

Short-time behavior for game-theoretic p-caloric functions

Asymptotics for the resolvent equation associated to the game-theoreticp-laplacian

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