Stochastic homogenization for functionals with anisotropic rescaling and noncoercive Hamilton--Jacobi equations

Dirr, Nicolas ORCID: https://orcid.org/0000-0003-3634-7367, Dragoni, Federica ORCID: https://orcid.org/0000-0001-6076-9725, Mannucci, Paola and Marchi, Claudio 2018. Stochastic homogenization for functionals with anisotropic rescaling and noncoercive Hamilton--Jacobi equations. SIAM Journal on Mathematical Analysis 50 (5) , pp. 5198-5242. 10.1137/17M1144428

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Abstract

We study the stochastic homogenization for a Cauchy problem for a first-order Hamilton--Jacobi equation whose operator is not coercive w.r.t. the gradient variable. We look at Hamiltonians like $H(x,\sigma(x)p,\omega)$, where $\sigma(x)$ is a matrix associated to a Carnot group. The rescaling considered is consistent with the underlying Carnot group structure, thus anisotropic. We will prove that under suitable assumptions for the Hamiltonian, the solutions of the $\varepsilon$-problem converge to a deterministic function which can be characterized as the unique (viscosity) solution of a suitable deterministic Hamilton--Jacobi problem.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Publisher:	Society for Industrial and Applied Mathematics
ISSN:	0036-1410
Funders:	EPSRC
Date of First Compliant Deposit:	18 August 2018
Date of Acceptance:	13 July 2018
Last Modified:	04 Dec 2024 19:00
URI:	https://orca.cardiff.ac.uk/id/eprint/114253

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