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

 Dirr, Nicolas, Dragoni, Federica, Marchi, Claudio and Mannucci, Paola 2018. Stochastic homogenization for functionals with anisotropic rescaling and non-coercive 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 Publication Published Mathematics Society for Industrial and Applied Mathematics 0036-1410 EPSRC 18 August 2018 13 July 2018 29 Jun 2019 10:32 http://orca.cf.ac.uk/id/eprint/114253

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