{"title":"Partial Data Inverse Problems for Magnetic Schrödinger Operators with Potentials of Low Regularity","authors":"Salem Selim","doi":"10.1137/22m1530707","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4594-4622, August 2024. <br/> Abstract. We establish a global uniqueness result for an inverse boundary problem with partial data for the magnetic Schrödinger operator with a magnetic potential of class [math], and an electric potential of class [math]. Our result is an extension, in terms of the regularity of the potentials, of the results [D. Dos Santos Ferreira et al., Comm. Math. Phys., 271 (2007), pp. 467–488] and [K. Knudsen and M. Salo, Inverse Probl. Imaging, 1 (2007), pp. 349–369]. As a consequence, we also show global uniqueness for a partial data inverse boundary problem for the advection-diffusion operator with the advection term of class [math].","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Mathematical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/22m1530707","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4594-4622, August 2024. Abstract. We establish a global uniqueness result for an inverse boundary problem with partial data for the magnetic Schrödinger operator with a magnetic potential of class [math], and an electric potential of class [math]. Our result is an extension, in terms of the regularity of the potentials, of the results [D. Dos Santos Ferreira et al., Comm. Math. Phys., 271 (2007), pp. 467–488] and [K. Knudsen and M. Salo, Inverse Probl. Imaging, 1 (2007), pp. 349–369]. As a consequence, we also show global uniqueness for a partial data inverse boundary problem for the advection-diffusion operator with the advection term of class [math].
期刊介绍：
SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena.
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