Hölder continuity for integro-differential parabolic equations with polynomial growth respect to the gradient

Discrete and Continuous Dynamical Systems

Volumn 28, Issue 3, 2010, Pages 1069-1081

  Silvestre, Luis ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

H lder regularity; Integro differential equations; Parabolic equations

Indexed keywords

EID: 77955317365     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2010.28.1069     Document Type: Article

References (7)

1. Luis Caffarelli and Luis Silvestre, Regularity theory for fully nonlinear integro-differential equations, Coram. Pure Appl. Math., 62 (2009), 597-638.
2. P. Cardaliaguet and C. Rainer, Hölder regularity for viscosity solutions of fully nonlinear, local or nonlocal, Hamilton-Jacobi equations with super-quadratic growth in the gradient, Arxiv preprint, 2010, arXiv:1001. S191
3. I. Capuzzo Dolcetta and A. Vitolo, On the maximum principle for viscosity solutions of fully nonlinear elliptic equations in general domains, Matematiche (Catania), 62 (2007), 69-91.
4. Cyril Imbert, A non-local regularization of first order Hamilton-Jacobi equations, J. Differential Equations, 211 (2005), 218-246.
5. L. Silvestre, On the differentiability of the solution to the Hamilton-Jacobi equation with critical fractional diffusion, Preprint, 2009, arXiv:0911.5147.
6. Luis Silvestre, Hölder estimates for solutions of integro-differential equations like the fractional Laplace, Indiana Univ. Math. J., 55 (2006), 1155-1174.
7. Neil S. Trudinger, Comparison principles and pointwise estimates for viscosity solutions of nonlinear elliptic equations, Rev. Mat. Iberoamericana, 4 (1988), 453-468.