PARABOLIC SYSTEMS WITH MEASURABLE COEFFICIENTS IN WEIGHTED SOBOLEV SPACES

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2 Citations (Scopus)

Abstract

We present a weighted Lp-theory of parabolic systems on a half space Rd+. The leading coefficients are assumed to be only measurable in time t and have small bounded mean oscillations (BMO) with respect to the spatial variables x, and the lower order coefficients are allowed to blow up near the boundary.

Original languageEnglish
Pages (from-to)2587-2613
Number of pages27
JournalCommunications on Pure and Applied Analysis
Volume21
Issue number8
DOIs
Publication statusPublished - 2022 Aug

Bibliographical note

Funding Information:
2020 Mathematics Subject Classification. 35K51, 35R05. Key words and phrases. sharp/maximal functions, parabolic systems, weighted Sobolev spaces, measurable coefficients. The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1A2C1084683).The second author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C1A01003354). The third author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1F1A1058988). ∗Corresponding author.

Publisher Copyright:
© 2022 American Institute of Mathematical Sciences. All rights reserved.

Keywords

  • measurable coefficients
  • parabolic systems
  • sharp/maximal functions
  • weighted Sobolev spaces

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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