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 language | English |
|---|---|
| Pages (from-to) | 6283-6307 |
| Number of pages | 25 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 365 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 2013 Oct 2 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics
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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 journal › Article
TY - JOUR
T1 - Neumann functions for second order elliptic systems with measurable coefficients
AU - Choi, Jongkeun
AU - Kim, Seick
PY - 2013/10/2
Y1 - 2013/10/2
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=84884686020&partnerID=8YFLogxK
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U2 - 10.1090/S0002-9947-2013-05886-2
DO - 10.1090/S0002-9947-2013-05886-2
M3 - Article
VL - 365
SP - 6283
EP - 6307
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 12
ER -