Boundary Estimates for Solutions of Free Boundary Problems

  • Darya Apushkinskaya
Part of the Lecture Notes in Mathematics book series (LNM, volume 2218)


In this chapter we concentrate only on our first main question about regularity properties of a solution.


  1. [Fri82]
    A. Friedman, Variational Principles and Free-Boundary Problems. Pure and Applied Mathematics (Wiley, New York, 1982). A Wiley-Interscience PublicationGoogle Scholar
  2. [LSU67]
    O.A. Ladyženskaja, V.A. Solonnikov, N.N. Uralceva, Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs, vol. 23 (American Mathematical Society, Providence, RI, 1967). Translated from the Russian by S. SmithGoogle Scholar
  3. [SUW09]
    H. Shahgholian, N. Uraltseva, G.S. Weiss, A parabolic two-phase obstacle-like equation. Adv. Math. 221(3), 861–881 (2009)MathSciNetCrossRefGoogle Scholar
  4. [Ura97]
    N.N. Uraltseva, On some properties of the free boundary in a neighborhood of the points of contact with a given boundary. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 249(Kraev. Zadachi Mat. Fiz. i Smezh. Vopr. Teor. Funkts. 29), 303–312 (1997)Google Scholar
  5. [Ura01]
    N.N. Uraltseva, Two-phase obstacle problem. J. Math. Sci. (New York) 106(3), 3073–3077 (2001). Function theory and phase transitionsGoogle Scholar
  6. [Wei01]
    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 Free Bound. 3(2), 121–128 (2001)MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

  • Darya Apushkinskaya
    • 1
  1. 1.Department of MathematicsSaarland UniversitySaarbrückenGermany

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