Convergence of Rothe's method for fully nonlinear parabolic equations
Analysis of PDEs
2025-10-20 v1 Numerical Analysis
Numerical Analysis
Abstract
Convergence of Rothe's method for the fully nonlinear parabolic equation u_t + F(D^2 u, Du, u, x, t) = 0 is considered under some continuity assumptions on F. We show that the Rothe solutions are Lipschitz in time, Holder in space, and they solve the equation in the viscosity sense. As an immediate corollary we get Lipschitz behavior in time of the viscosity solutions of our equation.
Keywords
Cite
@article{arxiv.math/0404424,
title = {Convergence of Rothe's method for fully nonlinear parabolic equations},
author = {I. Blank and P. Smith},
journal= {arXiv preprint arXiv:math/0404424},
year = {2025}
}
Comments
13 pages, 1 figure, latex