Journal of Inequalities and Applications
Volume 1 (1997), Issue 1, Pages 73-83
Stability of Lipschitz type in determination of initial heat distribution
1Department of Mathematics, Faculty of Engineering Gunma University, Kiryu 376, Japan
2Department of Mathematical Sciences, The University of Tokyo Komaba, Meguro, Tokyo 153, Japan
Received 12 February 1996
Copyright © 1997 Saburou Saitoh and Masahiro Yamamoto. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
For the solution
of the equations
, is a bounded domain with
-boundary and for an appropriate subboundary
we prove a Lipschitz estimate of
: For and for a positive constant
The norm is involved and strong, but it is a natural one in our situation relating to a typical and simple norm for analytic functions. Furthermore, it is acceptable in the sense that holds.