We establish the optimal regularity (of class W 2∞ ) of a solution to the two-phase obstacle problem
with a nonhomogeneous Dirichlet condition in a bounded domain Ω ⊂ ℝn with smooth boundary ∂Ω. Bibliography: 10 titles.
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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 (2001), 121–128.
R. Jensen, “Boundary regularity for variational inequalities,” Indiana Univ. Math. J. 29 (1980), no. 4, 495–504.
N. N. Uraltseva, “Two-phase obstacle problem” [in Russian], Probl. Mat. Anal. 22 (2001), 240–245; English transl.: J. Math. Sci. (New York) 106 (2001), 3073–3077.
H. Shahgholian, “C 1,1-regularity in semilinear elliptic problems,” Comm. Pure Appl. Math. 56 (2003), 278–281.
J. Andersson, N. Matevosyan, and H. Mikayelyan, “On the tangential touch between the free and the fixed boundaries for the two-phase obstacle-like problem,” Ark. Mat. 44 (2006), 1–15.
N. N. Uraltseva, “Boundary estimates for solutions of elliptic and parabolic equations with discontinuous nonlinearities,” Am. Math. Soc. Transl. (2). [To appear]
H. W. Alt, L. A. Caffarelli, and A. Friedman, “Variational problems with two phases and their free boundaries,” Trans. Amer. Math. Soc. 282 (1984), no. 2, 431–461.
Translated from Problemy Matematicheskogo Analiza, No. 34, 2006, pp. 3–11.
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Apushkinskaya, D.E., Uraltseva, N.N. Boundary estimates for solutions of two-phase obstacle problems. J Math Sci 142, 1723–1732 (2007). https://doi.org/10.1007/s10958-007-0083-8
- Free Boundary
- Obstacle Problem
- Boundary Estimate
- Homogenous Dirichlet Boundary Condition
- Optimal Regularity