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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Dirichlet problem for degenerate elliptic equations
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by Avner Friedman and Mark A. Pinsky PDF
Trans. Amer. Math. Soc. 186 (1973), 359-383 Request permission

Abstract:

Let ${L_0}$ be a degenerate second order elliptic operator with no zeroth order term in an m-dimensional domain G, and let $L = {L_0} + c$. One divides the boundary of G into disjoint sets ${\Sigma _1},{\Sigma _2},{\Sigma _3};{\Sigma _3}$ is the noncharacteristic part, and on ${\Sigma _2}$ the “drift” is outward. When c is negative, the following Dirichlet problem has been considered in the literature: $Lu = 0$ in G, u is prescribed on ${\Sigma _2} \cup {\Sigma _3}$. In the present work it is assume that $c \leq 0$. Assuming additional boundary conditions on a certain finite number of points of ${\Sigma _1}$, a unique solution of the Dirichlet problem is established.
References
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 186 (1973), 359-383
  • MSC: Primary 35J70; Secondary 60H15
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0328345-2
  • MathSciNet review: 0328345