Back to Search Start Over

H^2-regularity for a two-dimensional transmission problem with geometric constraint

H^2-regularity for a two-dimensional transmission problem with geometric constraint

Authors :
Philippe Laurençot
Christoph Walker
Institut de Mathématiques de Toulouse UMR5219 (IMT)
Institut National des Sciences Appliquées - Toulouse (INSA Toulouse)
Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)
Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3)
Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)
Institut fur angewandte mathematik, Leibniz Universitat Hannover
Leibniz Universität Hannover [Hannover] (LUH)
Université Toulouse Capitole (UT Capitole)
Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse)
Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)
Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3)
Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
Leibniz Universität Hannover=Leibniz University Hannover
Source :
Mathematische Zeitschrift 302 (2022), Nr. 3, Mathematische Zeitschrift, Mathematische Zeitschrift, 2022, 302, pp.1879--1904
Publication Year :
2021
Publisher :
HAL CCSD, 2021.

Abstract

The $$H^2$$ H 2 -regularity of variational solutions to a two-dimensional transmission problem with geometric constraint is investigated, in particular when part of the interface becomes part of the outer boundary of the domain due to the saturation of the geometric constraint. In such a situation, the domain includes some non-Lipschitz subdomains with cusp points, but it is shown that this feature does not lead to a regularity breakdown. Moreover, continuous dependence of the solutions with respect to the domain is established.

Details

Language :
English
ISSN :
00255874 and 14321823
Database :
OpenAIRE
Journal :
Mathematische Zeitschrift 302 (2022), Nr. 3, Mathematische Zeitschrift, Mathematische Zeitschrift, 2022, 302, pp.1879--1904
Accession number :
edsair.doi.dedup.....f8933264a249fdfc8f6cba8a806a4418