Hölder estimates in space-time for viscosity solutions of Hamilton-Jacobi equations
Cannarsa, Piermarco; Cardaliaguet, Pierre (2010), Hölder estimates in space-time for viscosity solutions of Hamilton-Jacobi equations, Communications on Pure and Applied Mathematics, 63, 5, p. 590-629. http://dx.doi.org/10.1002/cpa.20315
Type
Article accepté pour publication ou publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00371681/fr/Date
2010Journal name
Communications on Pure and Applied MathematicsVolume
63Number
5Publisher
Wiley
Pages
590-629
Publication identifier
Metadata
Show full item recordAbstract (EN)
It is well-known that solutions to the basic problem in the calculus of variations may fail to be Lipschitz-continuous when the Lagrangian depends on t. Similarly, for viscosity solutions to time-dependent Hamilton-Jacobi equations one cannot expect Lipschitz bounds to hold uniformly with respect to the regularity of coefficients. This phenomenon raises the question whether such solutions satisfy uniform estimates in some weaker norm. We will show that this is the case for a suitable Hölder norm, obtaining uniform estimates in (x,t) for solutions to first- and second-order Hamilton-Jacobi equations. Our results apply to degenerate parabolic equations and require superlinear growth at infinity, in the gradient variables, of the Hamiltonian. Proofs are based on comparison arguments and representation formulas for viscosity solutions, as well as weak reverse Hölder inequalities.Subjects / Keywords
Hamilton-Jacobi equations; viscosity solutions; Hölder continuity; degenerate parabolic equations; reverse Hölder inequalitiesRelated items
Showing items related by title and author.
-
Cardaliaguet, Pierre; Rainer, Catherine (2011) Article accepté pour publication ou publié
-
Crandall, Michael G.; Lions, Pierre-Louis (1985) Article accepté pour publication ou publié
-
Error estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations Armstrong, Scott N.; Cardaliaguet, Pierre; Souganidis, Panagiotis E. (2014) Article accepté pour publication ou publié
-
Crandall, Michael G.; Lions, Pierre-Louis (1991) Article accepté pour publication ou publié
-
Crandall, Michael G.; Lions, Pierre-Louis (1990) Article accepté pour publication ou publié