Exact and approximate correctors for stochastic Hamiltonians: The 1-dimensional case
type: Item
instance of: scholarly article
title: Exact and approximate correctors for stochastic Hamiltonians: The 1-dimensional case
zbMATH Open document ID: 1191.37044
author: Andrea Davini
author: Antonio Siconolfi
published in: Mathematische Annalen
publication date: 2009-10-14T00:00:00Z
review text: Given a \(1-\) dimensional ergodic dynamical system \((\tau_x)_{x\in \mathbb{R}}\) on a probability space \((\Omega, F,P)\), it is considered a stationary Hamiltonian \(H(x,p,\omega),\) defined in \(\mathbb{R}\times \mathbb{R}\times\Omega,\) enjoying suitable continuity, quasiconvexity and coercivity conditions, and the family of stochastic Hamilton-Jacobi equations \[ H(x, v^{\prime}(x,\omega),\omega)=a. \] The authors perform a qualitative investigation of critical Hamilton-Jacobi equations: show the existence of approximate correctors, give characterizing conditions for the existence of correctors, provide Lax-type representation formulae and establish comparison principles.
reviewed by: Nasir N. Ganikhodjaev
Mathematics Subject Classification ID: 37L55
zbMATH DE Number: 5614926
zbMATH Keywords: Hamilton-Jacobi equations
zbMATH Keywords: corrector
zbMATH Keywords: Lax-type representation
zbMATH Keywords: homogenization problem
MaRDI profile type: Publication
full work available at URL: s00208-009-0372-2
OpenAlex ID: W2088163787
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DOI: 10.1007/S00208-009-0372-2
description: scientific article; zbMATH DE number 5614926