{"title":"Existence of critical points for a mean field functional on a compact Riemann surface with boundary","authors":"Mengjie Zhang, Y. Yang","doi":"10.4064/sm210922-11-3","DOIUrl":"https://doi.org/10.4064/sm210922-11-3","url":null,"abstract":"","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Derivations mapping into scattered operators","authors":"Peng Cao, Sen Zhu","doi":"10.4064/sm220205-24-2","DOIUrl":"https://doi.org/10.4064/sm220205-24-2","url":null,"abstract":"","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70524916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Closed ideals in weighted big Lipschitz algebras of analytic functions","authors":"B. Bouya, M. Zarrabi","doi":"10.4064/sm210401-25-10","DOIUrl":"https://doi.org/10.4064/sm210401-25-10","url":null,"abstract":"","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70515748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Embedding of fractional Sobolev spaces is equivalent to regularity of the measure","authors":"P. Górka, Artur Słabuszewski","doi":"10.4064/sm220304-2-7","DOIUrl":"https://doi.org/10.4064/sm220304-2-7","url":null,"abstract":"","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70524822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Approximation properties in terms of Lipschitz maps","authors":"Mingu Jung, Ju Myung Kim","doi":"10.4064/sm220314-19-8","DOIUrl":"https://doi.org/10.4064/sm220314-19-8","url":null,"abstract":"","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70526307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In this paper, the Monge–Kantorovich problem is considered in infinite dimensions on an abstract Wiener space ( W, H, µ ) , where H is the Cameron–Martin space and µ is the Gaussian measure. We study the regularity of optimal transport maps with a quadratic cost function assuming that both initial and target measures have a strictly positive Radon–Nikodym density with respect to µ . Under some conditions on the density functions, the forward and backward transport maps can be written in terms of Sobolev derivatives of so-called Monge–Brenier maps, or Monge potentials. We show the Sobolev regularity of the backward potential under the assumption that the density of the initial measure is log-concave and prove that the backward potential solves the Monge–Ampère equation.
{"title":"Regularity of the backward Monge potential and the Monge–Ampère equation on Wiener space","authors":"M. Çağlar, I. Demirel","doi":"10.4064/sm210906-2-5","DOIUrl":"https://doi.org/10.4064/sm210906-2-5","url":null,"abstract":". In this paper, the Monge–Kantorovich problem is considered in infinite dimensions on an abstract Wiener space ( W, H, µ ) , where H is the Cameron–Martin space and µ is the Gaussian measure. We study the regularity of optimal transport maps with a quadratic cost function assuming that both initial and target measures have a strictly positive Radon–Nikodym density with respect to µ . Under some conditions on the density functions, the forward and backward transport maps can be written in terms of Sobolev derivatives of so-called Monge–Brenier maps, or Monge potentials. We show the Sobolev regularity of the backward potential under the assumption that the density of the initial measure is log-concave and prove that the backward potential solves the Monge–Ampère equation.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On a one-parameter continuous family of pairs of complementary boundary conditions","authors":"A. Bobrowski, Elżbieta Ratajczyk","doi":"10.4064/sm210618-3-11","DOIUrl":"https://doi.org/10.4064/sm210618-3-11","url":null,"abstract":"","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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