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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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Neumann functions for second order elliptic systems with measurable coefficients
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by Jongkeun Choi and Seick Kim PDF
Trans. Amer. Math. Soc. 365 (2013), 6283-6307 Request permission

Abstract:

We study Neumann functions for divergence form, second-order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We establish existence, uniqueness, and various estimates for the Neumann functions under the assumption that weak solutions of the system enjoy interior Hölder continuity. Also, we establish global pointwise bounds for the Neumann functions under the assumption that weak solutions of the system satisfy a certain natural local boundedness estimate. Moreover, we prove that such a local boundedness estimate for weak solutions of the system is in fact equivalent to the global pointwise bound for the Neumann function. We present a unified approach valid for both the scalar and the vectorial cases.
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Additional Information
  • Jongkeun Choi
  • Affiliation: Department of Mathematics, Yonsei University, Seoul 120-749, Republic of Korea
  • Email: cjg@yonsei.ac.kr
  • Seick Kim
  • Affiliation: Department of Mathematics, Yonsei University, Seoul 120-749, Republic of Korea
  • Address at time of publication: Department of Computational Science and Engineering, Yonsei University, Seoul 120-749, Republic of Korea
  • MR Author ID: 707903
  • Email: kimseick@yonsei.ac.kr
  • Received by editor(s): July 2, 2011
  • Received by editor(s) in revised form: March 11, 2012
  • Published electronically: June 3, 2013
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 365 (2013), 6283-6307
  • MSC (2010): Primary 35J08, 35J47, 35J57
  • DOI: https://doi.org/10.1090/S0002-9947-2013-05886-2
  • MathSciNet review: 3105752