A W2n-theory of elliptic and parabolic partial differential systems in C 1 domains

Kyeong Hun Kim; Kijung Lee

doi:10.1016/j.jmaa.2012.02.061

A W2n-theory of elliptic and parabolic partial differential systems in C ¹ domains

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we consider the second-order parabolic partial differential systems and elliptic systems with C ¹ space domains. We prove the existence and uniqueness results in the Sobolev spaces with weights. In this solution spaces the derivatives of solutions are allowed to blow up near the boundary and also the coefficients of the systems may oscillate to a great extent or blow up near the boundary.

Original language	English
Pages (from-to)	397-414
Number of pages	18
Journal	Journal of Mathematical Analysis and Applications
Volume	391
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2012.02.061
Publication status	Published - 2012 Jul 15

Bibliographical note

Funding Information:
E-mail addresses: [email protected] (K.-H. Kim), [email protected] (K. Lee). 1 The research of this author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0015961). 2 The research of this author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0005597).

Keywords

Elliptic systems
Parabolic systems
Weighted Sobolev spaces

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2012.02.061

Cite this

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title = "A W2n-theory of elliptic and parabolic partial differential systems in C 1 domains",

abstract = "In this paper we consider the second-order parabolic partial differential systems and elliptic systems with C 1 space domains. We prove the existence and uniqueness results in the Sobolev spaces with weights. In this solution spaces the derivatives of solutions are allowed to blow up near the boundary and also the coefficients of the systems may oscillate to a great extent or blow up near the boundary.",

keywords = "Elliptic systems, Parabolic systems, Weighted Sobolev spaces",

author = "Kim, {Kyeong Hun} and Kijung Lee",

note = "Funding Information: E-mail addresses: [email protected] (K.-H. Kim), [email protected] (K. Lee). 1 The research of this author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0015961). 2 The research of this author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0005597).",

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AU - Lee, Kijung

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PY - 2012/7/15

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N2 - In this paper we consider the second-order parabolic partial differential systems and elliptic systems with C 1 space domains. We prove the existence and uniqueness results in the Sobolev spaces with weights. In this solution spaces the derivatives of solutions are allowed to blow up near the boundary and also the coefficients of the systems may oscillate to a great extent or blow up near the boundary.

AB - In this paper we consider the second-order parabolic partial differential systems and elliptic systems with C 1 space domains. We prove the existence and uniqueness results in the Sobolev spaces with weights. In this solution spaces the derivatives of solutions are allowed to blow up near the boundary and also the coefficients of the systems may oscillate to a great extent or blow up near the boundary.

KW - Elliptic systems

KW - Parabolic systems

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