Abstract:
For a simple elliptic obstacle problem the behaviour of the free boundary is studied near its points of contact with the fixed boundary of the domain. An earlier result of the author on the C1-regularity of the boundary ∂N of the non-coincidence set is refined. It is shown that the previously imposed Lipschitz condition on ∂N can be dispensed with.
\Bibitem{Ura00}
\by N.~N.~Ural'tseva
\paper Contact of a~free boundary with a~fixed boundary
\jour Sb. Math.
\yr 2000
\vol 191
\issue 2
\pages 307--315
\mathnet{http://mi.mathnet.ru/eng/sm457}
\crossref{https://doi.org/10.1070/sm2000v191n02ABEH000457}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1751779}
\zmath{https://zbmath.org/?q=an:0956.35139}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000087494000012}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0034341435}
Linking options:
https://www.mathnet.ru/eng/sm457
https://doi.org/10.1070/sm2000v191n02ABEH000457
https://www.mathnet.ru/eng/sm/v191/i2/p165
This publication is cited in the following 2 articles:
D. E. Apushkinskaya, A. A. Arkhipova, V. M. Babich, G. S. Weiss, I. A. Ibragimov, S. V. Kislyakov, N. V. Krylov, A. A. Laptev, A. I. Nazarov, G. A. Seregin, T. A. Suslina, H. Shahgholian, “On the 90th birthday of Nina Nikolaevna Uraltseva”, Russian Math. Surveys, 79:6 (2024), 1119–1131
Shahgholian H., Uraltseva N., “Regularity properties of a free boundary near contact points with the fixed boundary”, Duke Math. J., 116:1 (2003), 1–34
Citation in format AMSBIB
Contact us: