Details
| Original language | English |
|---|---|
| Pages (from-to) | 1879-1904 |
| Number of pages | 26 |
| Journal | Mathematische Zeitschrift |
| Volume | 302 |
| Issue number | 3 |
| Early online date | 7 Sept 2022 |
| Publication status | Published - Nov 2022 |
Abstract
The H2-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.
Keywords
- Non-Lipschitz domain, Regularity, Transmission problem
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Mathematische Zeitschrift, Vol. 302, No. 3, 11.2022, p. 1879-1904.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - H2-regularity for a two-dimensional transmission problem with geometric constraint
AU - Laurençot, Philippe
AU - Walker, Christoph
PY - 2022/11
Y1 - 2022/11
N2 - The H2-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.
AB - The H2-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.
KW - Non-Lipschitz domain
KW - Regularity
KW - Transmission problem
UR - http://www.scopus.com/inward/record.url?scp=85137460654&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2103.07301
DO - 10.48550/arXiv.2103.07301
M3 - Article
AN - SCOPUS:85137460654
VL - 302
SP - 1879
EP - 1904
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 3
ER -