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Hölder Regularity for Viscosity Solutions of Fully Nonlinear, Local or Nonlocal, Hamilton–Jacobi Equations with Superquadratic Growth in the Gradient

Cardaliaguet, Pierre; Rainer, Catherine (2011), Hölder Regularity for Viscosity Solutions of Fully Nonlinear, Local or Nonlocal, Hamilton–Jacobi Equations with Superquadratic Growth in the Gradient, SIAM Journal on Control and Optimization, 49, 2, p. 555-573. http://dx.doi.org/10.1137/100784400

Type
Article accepté pour publication ou publié
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http://hal.archives-ouvertes.fr/hal-00451248/fr/
Date
2011
Nom de la revue
SIAM Journal on Control and Optimization
Volume
49
Numéro
2
Éditeur
SIAM
Pages
555-573
Identifiant publication
Métadonnées
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Auteur(s)
Cardaliaguet, Pierre
Rainer, Catherine
Résumé (EN)
Viscosity solutions of fully nonlinear, local or nonlocal, Hamilton–Jacobi equations with a superquadratic growth in the gradient variable are proved to be Hölder continuous, with a modulus depending only on the growth of the Hamiltonian. The proof involves some representation formula for nonlocal Hamilton–Jacobi equations in terms of controlled jump processes and a weak reverse Hölder inequality.
Mots-clés
integro-differential Hamilton–Jacobi equations; viscosity solutions; Hölder continuity; degenerate parabolic equations; reverse Hölder inequalities