Convergence of Rothe's method for fully nonlinear parabolic equations

Details Convergence of Rothe's method for fully nonlinear parabolic equations Convergence of Rothe's method for fully nonlinear parabolic equations

2004-04-23

arxiv.org/abs/math/0404424v1

Mathematics

Analysis of PDEs

13 pages, 1 figure, latex

Scientific paper

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.

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