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

Kyeong Hun Kim, Kijung Lee

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)397-414
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Volume391
Issue number2
DOIs
Publication statusPublished - 2012 Jul 15

Bibliographical note

Funding Information:
E-mail addresses: kyeonghun@korea.ac.kr (K.-H. Kim), kijung@ajou.ac.kr (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

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