Convergence of Rothe's method for fully nonlinear parabolic equations |
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| Authors: | Ivan Blank Penelope Smith |
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| Affiliation: | (1) Department of Mathematics, Worcester Polytechnic Institute, 01609 Worcester, MA;(2) Department of Mathematics, Lehigh University, 18015 Bethlehem, PA |
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| Abstract: | Convergence of Rothe's method for the fully nonlinear parabolic equation ut+F(D2u, Du, u, x, t)=0 is considered under some continuity assumptions on F. We show that the Rothe solutions are Lipschitz in time, Hölder 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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| Keywords: | KeywordHeading" >Math Subject Classifications 35J60 65M20 |
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