Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Maximum principles for degenerate elliptic-parabolic equations with Venttsel's boundary condition

Author: Kazuo Amano
Journal: Trans. Amer. Math. Soc. 263 (1981), 377-396
MSC: Primary 35J70; Secondary 35B50, 58G32, 60J60
MathSciNet review: 594415
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Abstract: In this paper, we first establish interior and boundary maximum principles for degenerate elliptic-parabolic equations; we state both principles in one single theorem in terms of the propagation set (cf. Theorem 1). We next generalize the boundary condition to Venttsel's one and obtain the similar result (cf. Theorem 2). Venttsel''s boundary condition contains Dirichlet, Neumann, oblique derivative and mixed boundary conditions as special cases and, from a probabilistic point of view (cf. Venttsel' [9]), it is the most general admissible boundary condition. We give several examples in the last section.

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Article copyright: © Copyright 1981 American Mathematical Society