IJPAM: Volume 67, No. 2 (2011)

UNIFORM LIPSCHITZ CONTINUITY OF SOLUTIONS
TO DISCRETE MORSE FLOWS

Yoshihiko Yamaura
Department of Mathematics
College of Humanities and Sciences
Nihon University
3-25-40, Sakurajosui, Setagaya-ku, Tokyo, 156-8550, JAPAN
e-mail: yamaura@math.chs.nihon-u.ac.jp


Abstract.The present paper shows Lipschitz continuity of discrete Morse (variational) flows to the regularized Alt-Caffarelli variational functional generating free boundaries; the continuity is uniform with respect to the discrete Morse flows and the regularization. Together with the uniform Hölder continuity shown in another paper, it is possible to construct Morse flows, which will be dealt with a forthcoming paper.

Received: December 27, 2010

AMS Subject Classification: 35J20

Key Words and Phrases: Bernstein method, Rothe's scheme, discrete Morse flows

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 67
Issue: 2