Existence and uniqueness of solutions to parabolic equations with superlinear Hamiltonians
Analysis of PDEs
2017-11-27 v3
Abstract
We give a proof of existence and uniqueness of viscosity solutions to parabolic quasilinear equations for a fairly general class of nonconvex Hamiltonians with superlinear growth in the gradient variable. The approach is mainly based on classical techniques for uniformly parabolic quasilinear equations and on the Lipschitz estimates proved in [S.N. Armstrong and H.V. Tran, Viscosity solutions of general viscous Hamilton-Jacobi equations, Math. Ann., 361 (2015)], as well as on viscosity solution arguments.
Keywords
Cite
@article{arxiv.1608.04043,
title = {Existence and uniqueness of solutions to parabolic equations with superlinear Hamiltonians},
author = {Andrea Davini},
journal= {arXiv preprint arXiv:1608.04043},
year = {2017}
}
Comments
21 pages. We have slightly changed the title and corrected some typos