Boundary estimates for solutions to the two-phase parabolic obstacle problem
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Estimates for the second-order derivatives of a solution to the two-phase parabolic obstacle problem are established. Similar results in the elliptic case were obtained by the authors in 2006. Bibliography: 4 titles.
KeywordsObstacle Problem Sobolev Norm Arbitrary Direction Boundary Estimate Singular Perturbation Problem
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- 1.D. E. Apushkinskaya, N. N. Uraltseva, “Boundary estimates for solutions of two-phase obstacle problems” [in Russian], Probl. Math. Anal. 34 (2006), 3–11; English transl.: J. Math. Sci. (New York) 142 (2007), 1723–1732.Google Scholar
- 3.H. Shahgholian, N. Uraltseva, G. Weiss, The Parabolic Two-Phase Membrane Problem: Regularity in Higher Dimensions, Preprint, http://www.citebase.org/abstract?id=oai:arXiv.org:0712.3411, 2007.
- 4.N. N. Uraltseva, “Boundary estimates for solutions of elliptic and parabolic equations with discontinuous nonlinearities,” In: Nonlinear Equations and Spectral Theory, Am. Math. Soc. Transl. (2) 220 (2007), 235–246.Google Scholar