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Information Journal Paper

Title

A TWO-PHASE FREE BOUNDARY PROBLEM FOR A SEMILINEAR ELLIPTIC EQUATION

Pages

  1067-1086

Abstract

 In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain DÌRn with smooth boundary. We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose Laplacians enjoy a certain inequality. We show that in dimension n=2, solutions have OPTIMAL GROWTH at non-isolated singular points, and the same result holds for n³3 under an (n-1) -dimensional density condition. Furthermore, we prove that the set of points in the SINGULAR SET that the solution does not have OPTIMAL GROWTH is locally countably (n-2) -rectiable.

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    • Cite

    APA: Copy

    AGHAJANI, ASADOLLAH. (2014). A TWO-PHASE FREE BOUNDARY PROBLEM FOR A SEMILINEAR ELLIPTIC EQUATION. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 40(5), 1067-1086. SID. https://sid.ir/paper/635849/en

    Vancouver: Copy

    AGHAJANI ASADOLLAH. A TWO-PHASE FREE BOUNDARY PROBLEM FOR A SEMILINEAR ELLIPTIC EQUATION. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2014;40(5):1067-1086. Available from: https://sid.ir/paper/635849/en

    IEEE: Copy

    ASADOLLAH AGHAJANI, “A TWO-PHASE FREE BOUNDARY PROBLEM FOR A SEMILINEAR ELLIPTIC EQUATION,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 40, no. 5, pp. 1067–1086, 2014, [Online]. Available: https://sid.ir/paper/635849/en

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