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 |
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Pages (from-to) | 397-414 |
Number of pages | 18 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 391 |
Issue number | 2 |
DOIs | |
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