Calculus of Variations and Geometric Measure Theory

A. Davini

Existence and uniqueness of solutions to parabolic equations with superlinear Hamiltonians

created by davini on 12 Jul 2023


Published Paper

Inserted: 12 jul 2023
Last Updated: 12 jul 2023

Journal: Commun. Contemp. Math.
Volume: 21
Number: 1
Year: 2019

ArXiv: 1608.04043 PDF


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.