Time Fractional Parabolic Equations with Measurable Coefficients and Embeddings for Fractional Parabolic Sobolev Spaces
- Authors
- Dong, Hongjie; Kim, Doyoon
- Issue Date
- 11월-2021
- Publisher
- OXFORD UNIV PRESS
- Citation
- INTERNATIONAL MATHEMATICS RESEARCH NOTICES, v.2021, no.22, pp.17563 - 17610
- Indexed
- SCIE
SCOPUS
- Journal Title
- INTERNATIONAL MATHEMATICS RESEARCH NOTICES
- Volume
- 2021
- Number
- 22
- Start Page
- 17563
- End Page
- 17610
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/135977
- DOI
- 10.1093/imrn/rnab229
- ISSN
- 1073-7928
- Abstract
- We consider time fractional parabolic equations in divergence and non-divergence form when the leading coefficients a(ij) are measurable functions of (t, x(1)) except for a(11), which is a measurable function of either t or x(1). We obtain the solvability in Sobolev spaces of the equations in the whole space, on a half space, and on a partially bounded domain. The proofs use a level set argument, a scaling argument, and embeddings in fractional parabolic Sobolev spaces for which we give a direct and elementary proof.
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