Abstract
For the parabolic obstacle problem with homogeneous Dirichlet boundary condition the regularity of the free boundary is studied in a neighborhood of the boundary of a domain. Bibliography: 6 titles.
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References
D. E. Apushkinskaya, H. Shahgholian, and N. N. Uraltseva, “Boundary estimates for solutions to the parabolic free boundary problem” [in Russian], Zap. Nauchn. Semin. POMI, 271 (2000), 39–55.
D. E. Apushkinskaya, H. Shahgholian, and N. N. Uraltseva, “On the Lipschitz property of the free boundary in the parabolic obstacle problem” [in Russian], Algebra Anal., 15 (2003), No. 3, 78–103.
H. Shahgholian and N. N. Uraltseva, “Regularity properties of a free boundary near contact point with the fix boundary,” Duke Math. J., 116 (2003), no. 1, 1–33.
O. A. Ladyzhenskaya and N. N. Uraltseva, “Boundary estimates of the first order derivatives of functions satisfying elliptic or parabolic inequality” [in Russian], Tr. MIAN, 179 (1988), 102–125.
G. S. Weiss, “Self-similar blow-up and Hausdorff dimension estimates for a class of parabolic free boundary problems”, SIAM J. Math. Anal., 30 (1999), No. 3, 623–644.
D. E. Apushkinskaya, H. Shahgholian, and N. N. Uraltseva, “On global solutions to the parabolic obstacle problem” [in Russian], Algebra Anal., 14 (2002), No. 1, 3–25.
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Galaktionova, N.E. Properties of Solutions to the Parabolic Obstacle Problem in a Neighborhood of the Boundary of a Domain. Journal of Mathematical Sciences 120, 1080–1092 (2004). https://doi.org/10.1023/B:JOTH.0000014837.15745.03
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DOI: https://doi.org/10.1023/B:JOTH.0000014837.15745.03