On the tangential touch between the free and the fixed boundaries for the two-phase obstacle-like problem

Preprint, Other literature type English OPEN
Andersson, John; Matevosyan, Norayr; Mikayelyan, Hayk;

In this paper we consider the following two-phase obstacle-problem-like equation in the unit half-ball $\Delta u = \lambda_{+\chi_{\{ u>0 \}}} - \lambda_{-\chi_{\{ u<0 \}}},\quad\lambda_{\pm}>0. $ We prove that the free boundary touches the fixed boundary (uniformly) ta... View more
  • References (12)
    12 references, page 1 of 2

    [ACF] H.W.Alt, L.A. Caffarelli, A. Friedman Variational problems with two phases and their free boundaries Trans. of AMS, Vol. 282, Nr. 2, 431-461

    [C] L.A. Caffarelli The obstacle problem revisited J. Fourier Analysis and Appl. 4 (1998), no. 4-5, 383-402

    [CKS] L.A. Caffarelli, L. Karp, H. Shahgholian Regularity of a free boundary with application to the Pompeiu problem Ann. of Math. (2) 151 (2000), no. 1, 269-292

    [M] N. Matevosyan Tangential touch between free and fixed boundaries Ph.D. thesis, KTH Stckholm, 2003

    [SU] H. Shahgholian, N.N. Uraltseva, Regularity properties of a free boundary near contact points with the fixed boundary, Duke math. J. 116 (2003), no. 1, 1-34

    [U] N.N. Uraltseva two-phase obstacle problem, Journal of Mathematical Sciences, Vol. 106, No. 3, 2001

    [W1] G.S. Weiss Partial regularity for a weak solutions of an elliptic free boundary problem Commun. in PDE, 23(3&4), 439-455 (1998)

    [W2] G.S. Weiss An obstacle-problem-like equation with two phases: pointwise regularity of the solution and an estimate of the Hausdorff dimension of the free boundary Interfaces and Free Boundaries, Vol. 3(2001), 121-128

    [Wi] K.-O. Widman Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations Math. Scand. 21, 1967, 17-37 (1968) John Andersson, Institutionen fo¨r Matematik, Kungliga Tekniska

    Ho¨gskolan, 100 44 Stockholm, Sweden E-mail address: johnan@e.kth.se Norayr Matevosyan, Johann Radon Institut fu¨r Angewandte Math-

  • Metrics
Share - Bookmark