Pub Date : 2026-01-01Epub Date: 2024-09-28DOI: 10.1007/s13348-024-00455-7
Stefan Fürdös, Gerhard Schindl
In 1978 Métivier showed that a linear differential operator P with analytic coefficients is elliptic if and only if the theorem of iterates holds for P with respect to any non-analytic Gevrey class. In this paper we extend this theorem to Denjoy-Carleman classes given by strongly non-quasianalytic weight sequences. The proof involves a new way to construct optimal functions in Denjoy-Carleman classes via Fourier integrals, which might be of independent interest. Moreover, we point out that the analogous statement for Braun-Meise-Taylor classes given by weight functions cannot hold. This signifies an important difference in the properties of Denjoy-Carleman classes and Braun-Meise-Taylor classes, respectively.
{"title":"Ellipticity and the problem of iterates in Denjoy-Carleman classes.","authors":"Stefan Fürdös, Gerhard Schindl","doi":"10.1007/s13348-024-00455-7","DOIUrl":"https://doi.org/10.1007/s13348-024-00455-7","url":null,"abstract":"<p><p>In 1978 Métivier showed that a linear differential operator <i>P</i> with analytic coefficients is elliptic if and only if the theorem of iterates holds for <i>P</i> with respect to any non-analytic Gevrey class. In this paper we extend this theorem to Denjoy-Carleman classes given by strongly non-quasianalytic weight sequences. The proof involves a new way to construct optimal functions in Denjoy-Carleman classes via Fourier integrals, which might be of independent interest. Moreover, we point out that the analogous statement for Braun-Meise-Taylor classes given by weight functions cannot hold. This signifies an important difference in the properties of Denjoy-Carleman classes and Braun-Meise-Taylor classes, respectively.</p>","PeriodicalId":72636,"journal":{"name":"Collectanea mathematica (Barcelona, Spain)","volume":"77 1","pages":"23-49"},"PeriodicalIF":0.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12909417/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146221789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1007/s13348-021-00348-z
Omar Sánchez
In this paper we study the existence of stationary solutions for the Muskat problem with a large surface tension coefficient. Ehrnstrom, Escher and Matioc studied in Mats Ehrnström (Methods Appl Anal 20:33-46, 2013) that there exists solutions to this problem for surface tensions below a finite value. In these notes we go beyond this value considering large surface tension. Also by numerical simulation we show some examples that explains the behavior of solutions.
{"title":"Steady-state solutions for the Muskat problem.","authors":"Omar Sánchez","doi":"10.1007/s13348-021-00348-z","DOIUrl":"https://doi.org/10.1007/s13348-021-00348-z","url":null,"abstract":"<p><p>In this paper we study the existence of stationary solutions for the Muskat problem with a large surface tension coefficient. Ehrnstrom, Escher and Matioc studied in Mats Ehrnström (Methods Appl Anal 20:33-46, 2013) that there exists solutions to this problem for surface tensions below a finite value. In these notes we go beyond this value considering large surface tension. Also by numerical simulation we show some examples that explains the behavior of solutions.</p>","PeriodicalId":72636,"journal":{"name":"Collectanea mathematica (Barcelona, Spain)","volume":"74 2","pages":"313-321"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10124092/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9719003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号