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: | 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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