Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Schwarz reflection principles for solutions of parabolic equations


Author: David Colton
Journal: Proc. Amer. Math. Soc. 82 (1981), 87-94
MSC: Primary 35B60; Secondary 35K10
DOI: https://doi.org/10.1090/S0002-9939-1981-0603607-X
MathSciNet review: 603607
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A reflection principle is obtained for solutions of the heat equation defined in a cylindrical domain of the form $ \Omega \times (0,T)$ where $ \Omega $ is a ball in $ {{\mathbf{R}}^n}$ and the solution vanishes on $ \partial \Omega \times (0,T)$. It is shown that the domain of dependence of the solution at a point outside the cylinder $ \Omega \times (0,T)$ is a line segment contained inside $ \Omega \times (0,T)$. In the case $ n = 2$ this result is generalized to the case of analytic solutions of parabolic equations with analytic coefficients defined in an arbitrary bounded simply connected cylinder $ D \times (0,T)$ where the solution vanishes on a portion of $ \partial D \times (0,T)$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35B60, 35K10

Retrieve articles in all journals with MSC: 35B60, 35K10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0603607-X
Article copyright: © Copyright 1981 American Mathematical Society