Poincaré-Type inequalities for green's operator on harmonic forms

Shusen Ding; Yuming Xing

doi:10.1007/978-1-4939-0808-0_7

Poincaré-Type inequalities for green's operator on harmonic forms

Shusen Ding^*
, Yuming Xing

^*Corresponding author for this work

School of Mathematics

Seattle University

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

In this paper, we prove the local Poincaré-type inequalities with singular factors for Green's operator applied to harmonic forms and extend the local results into the global cases in John domains. We also establish the local Poincaré-type inequalities with Orlicz norms for Green's operator on harmonic forms and global inequalities in L φ (m) -Averaging or averaging domains.

Original language	English
Title of host publication	Optimization in Science and Engineering
Publisher	Springer New York
Pages	141-155
Number of pages	15
Volume	9781493908080
ISBN (Electronic)	9781493908080
ISBN (Print)	1493908073, 9781493908073
DOIs	https://doi.org/10.1007/978-1-4939-0808-0_7
State	Published - 1 Jul 2014

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abstract = "In this paper, we prove the local Poincar{\'e}-type inequalities with singular factors for Green's operator applied to harmonic forms and extend the local results into the global cases in John domains. We also establish the local Poincar{\'e}-type inequalities with Orlicz norms for Green's operator on harmonic forms and global inequalities in L φ (m) -Averaging or averaging domains.",

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PY - 2014/7/1

Y1 - 2014/7/1

N2 - In this paper, we prove the local Poincaré-type inequalities with singular factors for Green's operator applied to harmonic forms and extend the local results into the global cases in John domains. We also establish the local Poincaré-type inequalities with Orlicz norms for Green's operator on harmonic forms and global inequalities in L φ (m) -Averaging or averaging domains.

AB - In this paper, we prove the local Poincaré-type inequalities with singular factors for Green's operator applied to harmonic forms and extend the local results into the global cases in John domains. We also establish the local Poincaré-type inequalities with Orlicz norms for Green's operator on harmonic forms and global inequalities in L φ (m) -Averaging or averaging domains.

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BT - Optimization in Science and Engineering

PB - Springer New York

ER -

Poincaré-Type inequalities for green's operator on harmonic forms

Abstract

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