Regularity theory for Hamilton--Jacobi equations
type: Item
instance of: scholarly article
title: Regularity theory for Hamilton--Jacobi equations
zbMATH Open document ID: 1023.35028
DOI: 10.1016/S0022-0396(02)00013-X
author: D. Gomes
published in: Journal of Differential Equations
publication date: 2003-03-18T00:00:00Z
review text: The author studies the regularity and stability under small perturbations of viscosity solutions of Hamilton-Jacobi equations \(H(P+D_x u, x)=\overline{H}(P),\) where \(H(p,x):\mathbb{R}^{2n}\rightarrow \mathbb{R}\) is a strictly convex smooth Hamiltonian (\(D^{2}_{vv} L(x,v)>\gamma >0\) uniformly and coercive in \(p, \lim_{|p|\rightarrow\infty} \frac{H(p,x)}{|p|}=\infty)\), \(\mathbb{Z}^{n}\) periodic in \(x\) \((H(p,x+k)=H(p,x)\), \(k\in \mathbb{Z}^{n})\) Analogs of the KAM theorem, stability of the viscosity solutions and Mather sets under small perturbations of the Hamiltonian are proved.
Mathematics Subject Classification ID: 35F20
Mathematics Subject Classification ID: 37J50
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 1884226
zbMATH Keywords: viscosity solutions
zbMATH Keywords: KAM theorem
zbMATH Keywords: Mather sets
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1884226