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Carleman estimates and boundedness of associated multiplier operators
DC Field | Value | Language |
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dc.contributor.author | Jeong, Eunhee | - |
dc.contributor.author | Kwon, Yehyun | - |
dc.contributor.author | Lee, Sanghyuk | - |
dc.date.accessioned | 2022-06-22T11:19:42Z | - |
dc.date.available | 2022-06-22T11:19:42Z | - |
dc.date.created | 2022-05-19 | - |
dc.date.issued | 2022-04 | - |
dc.identifier.citation | Communications in Partial Differential Equations, Vol.47 No.4, pp.774-796 | - |
dc.identifier.issn | 0360-5302 | - |
dc.identifier.uri | https://hdl.handle.net/10371/183193 | - |
dc.description.abstract | Let P(D) be the Laplacian Delta, or the wave operator square. The following type of Carleman estimate is known to be true on a certain range of p, q: parallel to e(v.x)u parallel to(Lq(Rd)) <= C parallel to e(v.x)P(D)u parallel to(Lp(Rd)) with C independent of v is an element of R-d. The estimates are consequences of the uniform Sobolev type estimates for second order differential operators due to Kenig-Ruiz-Sogge [1] and Jeong-Kwon-Lee [2]. The range of p, q for which the uniform Sobolev type estimates hold was completely characterized for the second order differential operators with nondegenerate principal part. But the optimal range of p, q for which the Carleman estimate holds has not been clarified before. When P(D) = Delta, square, or the heat operator, we obtain a complete characterization of the admissible p, q for the aforementioned type of Carleman estimate. For this purpose we investigate L-p-L-q boundedness of related multiplier operators. As applications, we also obtain some unique continuation results. | - |
dc.language | 영어 | - |
dc.publisher | Marcel Dekker Inc. | - |
dc.title | Carleman estimates and boundedness of associated multiplier operators | - |
dc.type | Article | - |
dc.identifier.doi | 10.1080/03605302.2021.2007532 | - |
dc.citation.journaltitle | Communications in Partial Differential Equations | - |
dc.identifier.wosid | 000741240100001 | - |
dc.identifier.scopusid | 2-s2.0-85122747148 | - |
dc.citation.endpage | 796 | - |
dc.citation.number | 4 | - |
dc.citation.startpage | 774 | - |
dc.citation.volume | 47 | - |
dc.description.isOpenAccess | N | - |
dc.contributor.affiliatedAuthor | Lee, Sanghyuk | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
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