AN L-p-LIPSCHITZ THEORY FOR PARABOLIC EQUATIONS WITH TIME MEASURABLE PSEUDO-DIFFERENTIAL OPERATORS
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Kim, Ildoo | - |
dc.date.accessioned | 2021-09-02T04:27:30Z | - |
dc.date.available | 2021-09-02T04:27:30Z | - |
dc.date.created | 2021-06-19 | - |
dc.date.issued | 2018-11 | - |
dc.identifier.issn | 1534-0392 | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/72079 | - |
dc.description.abstract | In this article we prove the existence and uniqueness of a (weak) solution u in L-p ((0; T); Lambda(gamma) +m) to the Cauchy problem partial derivative u/partial derivative t (t; x) = psi(t; i del) u (t; x) + f (t; x); (t; x) is an element of (0; T) R-d u (0; x) = 0; (1) where d is an element of N, p is an element of (1;infinity], Lambda(gamma+m) 2 (0;1), Lambda(gamma+m) is the Lipschitz space on R-d whose order is (gamma+m), f is an element of L-p ((0; T);Lambda(gamma) ), and psi(t; i del) is a time measurable pseudo-di ff erential operator whose symbol is (t; ), i. e. (t; ir) u (t; x) = F [(t; ) F [u (t; )] ()] (x); with the assumptions < [(t; )] and jDff (t; ) j : Furthermore, we show Z T 0 ku (t; ) k Lambda(gamma+m) dt <= N Z T 0 kf (t; ) k p m dt; (2) where N is a positive constant depending only on d,Lambda(gamma+m), and T, The unique solvability of equation (1) in Lp -H older space is also considered. More precisely, for any f 2 Lp ((0; T); Cn+ff), there exists a unique solution u 2 Lp ((0; T); C+n+ff (Rd)) to equation (1) and for this solution u, Z T 0 ku (t; ) k p C+n+ff dt N Z T 0 kf (t; ) k p Cn+ff dt; (3) where n is an element of Z(+), alpha is an element of (0; 1), and gamma + alpha is not an element of Z(+) | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | AMER INST MATHEMATICAL SCIENCES-AIMS | - |
dc.title | AN L-p-LIPSCHITZ THEORY FOR PARABOLIC EQUATIONS WITH TIME MEASURABLE PSEUDO-DIFFERENTIAL OPERATORS | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Kim, Ildoo | - |
dc.identifier.doi | 10.3934/cpaa.2018130 | - |
dc.identifier.scopusid | 2-s2.0-85056889402 | - |
dc.identifier.wosid | 000446346500025 | - |
dc.identifier.bibliographicCitation | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v.17, no.6, pp.2751 - 2771 | - |
dc.relation.isPartOf | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | - |
dc.citation.title | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | - |
dc.citation.volume | 17 | - |
dc.citation.number | 6 | - |
dc.citation.startPage | 2751 | - |
dc.citation.endPage | 2771 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.subject.keywordAuthor | Time measurable pseudo-differential operator | - |
dc.subject.keywordAuthor | L-p-Lipschitz estimate | - |
dc.subject.keywordAuthor | Cauchy problem | - |
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