A WEIGHTED L-p-THEORY FOR SECOND-ORDER PARABOLIC AND ELLIPTIC PARTIAL DIFFERENTIAL SYSTEMS ON A HALF SPACE
- Authors
- Kim, Kyeong-Hun; Lee, Kijung
- Issue Date
- 5월-2016
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- Keywords
- Elliptic partial differential systems; parabolic partial differential systems; weighted Sobolev spaces; L-p-theory; Fefferman-Stein theorem; Hardy-Littlewood theorem; sharp function estimates.
- Citation
- COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v.15, no.3, pp.761 - 794
- Indexed
- SCIE
SCOPUS
- Journal Title
- COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
- Volume
- 15
- Number
- 3
- Start Page
- 761
- End Page
- 794
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/88844
- DOI
- 10.3934/cpaa.2016.15.761
- ISSN
- 1534-0392
- Abstract
- this article we consider parabolic systems and L-p regularity of the solutions. With zero boundary condition the solutions experience bad regularity near the boundary. This article addresses a possible way of describing the regularity nature. Our space domain is a half space and we adapt an appropriate weight into our function spaces. In this weighted Sobolev space setting we develop a Fefferman-Stein theorem, a Hardy-Littlewood theorem and sharp function estimations. Using these, we prove uniqueness and existence results for second-order elliptic and parabolic partial differential systems in weighed Sobolev spaces.
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