Communications in Mathematical Sciences
Volume 16 (2018)
De Giorgi techniques applied to Hamilton–Jacobi equations with unbounded right-hand side
Pages: 1465 – 1487
In this article we obtain Holder estimates for solutions to second-order Hamilton–Jacobi equations with super-quadratic growth in the gradient and unbounded source term. The estimates are uniform with respect to the smallness of the diffusion and the smoothness of the Hamiltonian. Our work is in the spirit of a result by P. Cardaliaguet and L. Silvestre [P. Cardaliaguet and L. Silvestre, Comm. Partial Differential Equations, 37(9):1668–1688, 2012]. We utilize De Giorgi’s method, which was introduced to this class of equations in [C.-H. Chan and A.F. Vasseur, ArXiv e-prints, November 2014].
Hamilton–Jacobi equation, Hölder regularity, De Giorgi method
2010 Mathematics Subject Classification
Copyright © 2018 Logan F. Stokols and Alexis F. Vasseur
A.F. Vasseur was partially supported by the NSF Grant DMS 1614918.
Received 7 March 2017
Accepted 25 July 2017
Published 7 February 2019