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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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Hypoellipticity of certain degenerate elliptic boundary value problems
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by Yakar Kannai PDF
Trans. Amer. Math. Soc. 217 (1976), 311-328 Request permission

Abstract:

The concept of hypoellipticity for degenerate elliptic boundary value problems is defined, and its relation with the hypoellipticity of certain pseudo-differential operators on the boundary is discussed (for second order equations). A theorem covering smoothness of solutions of boundary value problems such as $a(x)\partial u/\partial n + b(x)u = f(x)$ for the Laplace equation is proved. An almost complete characterization of hypoelliptic boundary value problems for elliptic second order equations in two dimensions is given via analysis of hypoelliptic pseudo-differential operators in one variable.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 217 (1976), 311-328
  • MSC: Primary 35H05
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0407436-4
  • MathSciNet review: 0407436