Neumann functions for second order elliptic systems with measurable coefficients

Jongkeun Choi, Seick Kim

Research output: Contribution to journalArticle

14 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)6283-6307
Number of pages25
JournalTransactions of the American Mathematical Society
Volume365
Issue number12
DOIs
Publication statusPublished - 2013 Oct 2

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Neumann function
Second-order Systems
Elliptic Systems
Weak Solution
Coefficient
Boundedness
Estimate
Lipschitz Domains
Lipschitz
Bounded Domain
Divergence
Interior
Existence and Uniqueness
Scalar
Valid
Graph in graph theory

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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Neumann functions for second order elliptic systems with measurable coefficients. / Choi, Jongkeun; Kim, Seick.

In: Transactions of the American Mathematical Society, Vol. 365, No. 12, 02.10.2013, p. 6283-6307.

Research output: Contribution to journalArticle

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AB - 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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