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The obstacle problem with singular coefficients near Dirichlet data
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-1316-7913
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2017 (English)In: Annales de l'Institut Henri Poincare. Analyse non linéar, ISSN 0294-1449, E-ISSN 1873-1430, Vol. 34, no 2, p. 293-334Article in journal (Refereed) Published
Abstract [en]

In this paper we study the behaviour of the free boundary close to its contact points with the fixed boundary B boolean AND {x1 = 0} in the obstacle type problem {div(x(1)(a) del u) = X-{u>0} in B+, u=0 on B boolean AND {x(1) = 0} where a < 1, B+ = B boolean AND {x(1) > 0}, B is the unit ball in R-n and n > 2 is an integer. Let Gamma = B+ boolean AND partial derivative{u > 0} be the free boundary and assume that the origin is a contact point, i.e. 0 epsilon (Gamma) over bar. We prove that the free boundary touches the fixed boundary uniformly tangentially at the origin, near to the origin it is the graph of a C-1 function and there is a uniform modulus of continuity for the derivatives of this function.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 34, no 2, p. 293-334
Keywords [en]
Free boundary, Obstacle problem, Singular coefficient, Regularity of free boundaries
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-242316DOI: 10.1016/j.anihpc.2015.12.003ISI: 000395848500002Scopus ID: 2-s2.0-85006632171OAI: oai:DiVA.org:kth-242316DiVA, id: diva2:1285823
Note

QC 20190205

Available from: 2019-02-05 Created: 2019-02-05 Last updated: 2019-02-05Bibliographically approved

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Shahgholian, Henrik

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