A Strong Maximum Principle for Parabolic Systems in a Convex Set with Arbitrary Boundary

Details A Strong Maximum Principle for Parabolic Systems in a Convex Set with Arbitrary Boundary A Strong Maximum Principle for Parabolic Systems in a Convex Set with Arbitrary Boundary

2009-11-24

arxiv.org/abs/0911.4526v1

Proc. Amer. Math. Soc. 138 (2010), 3179-3185

Mathematics

Analysis of PDEs

7 pages, 0 figures. Submitted to the Proceedings of the American Mathematical Society

Scientific paper

In this paper we prove a strong maximum principle for certain parabolic systems of equations. In particular, our methods place no restriction on the regularity of the boundary of the convex set in which the system takes its values, and therefore our results hold for any convex set. We achieve this through the use of viscosity solutions and their corresponding strong maximum principle.

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