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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Indefinite elliptic boundary value problems on irregular domains
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by Jacqueline Fleckinger and Michel L. Lapidus PDF
Proc. Amer. Math. Soc. 123 (1995), 513-526 Request permission

Abstract:

We establish estimates for the remainder term of the asymptotics of the Dirichlet or Neumann eigenvalue problem \[ - \Delta u(x) = \lambda r(x)u(x),\quad x \in \Omega \subset {\mathbb {R}^n},\] defined on the bounded open set $\Omega \subset {\mathbb {R}^n}$; here, the "weight" r is a real-valued function on $\Omega$ which is allowed to change sign in $\Omega$ and the boundary $\partial \Omega$ is irregular. We even obtain error estimates when the boundary is "fractal". These results—which extend earlier work of the authors [particularly, J. Fleckinger & M. L. Lapidus, Arch. Rational Mech. Anal. 98 (1987), 329-356; M. L. Lapidus, Trans. Amer. Math. Soc. 325 (1991), 465-529]—are already of interest in the special case of positive weights.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 513-526
  • MSC: Primary 35P15; Secondary 28A75, 35J25, 47F05
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1231296-2
  • MathSciNet review: 1231296