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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Maximum principles for degenerate elliptic-parabolic equations with Venttsel’s boundary condition
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by Kazuo Amano PDF
Trans. Amer. Math. Soc. 263 (1981), 377-396 Request permission

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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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 263 (1981), 377-396
  • MSC: Primary 35J70; Secondary 35B50, 58G32, 60J60
  • DOI: https://doi.org/10.1090/S0002-9947-1981-0594415-1
  • MathSciNet review: 594415