Quasiderivatives and Interior Smoothness of Harmonic Functions Associated with Degenerate Diffusion Processes

N.V. Krylov (University of Minnesota)

Abstract


Proofs and two applications of two general results are given concerning the problem of establishing interior smoothness of probabilistic solutions of elliptic degenerate equations.

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Pages: 615-633

Publication Date: September 13, 2004

DOI: 10.1214/EJP.v9-219

References

    Alkhutov, Yu. A. The behavior of solutions of parabolic second-order equations in noncylindrical domains. (Russian) Dokl. Akad. Nauk 345 (1995), no. 5, 583--585. MR1376452 (97h:35073)

    Dong, Hongjie About smoothness of solutions of the heat equations in closed smooth space-time domains. Submitted to Comm. Pure Appl. Math.

    Freui dlin, M. I. The smoothness of the solutions of degenerate elliptic equations. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 32 1968 1391--1413. MR0237944 (38 #6221)

    Kohn, J. J.; Nirenberg, L. Degenerate elliptic-parabolic equations of second order. Comm. Pure Appl. Math. 20 1967 797--872. MR0234118 (38 #2437)

    Kondratcprime ev, V. A. Boundary value problems for parabolic equations in closed regions. (Russian) Trudy Moskov. Mat. Obv sv c. 15 1966 400--451. MR0209682 (35 #579)

    Krylov, N. V. Smoothness of the payoff function for a controllable diffusion process in a domain. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989), no. 1, 66--96; translation in Math. USSR-Izv. 34 (1990), no. 1, 65--95 MR0992979 (90f:93040)

    Krylov, N. V. On the first quasiderivatives of solutions of Itô stochastic equations. (Russian) Izv. Ross. Akad. Nauk Ser. Mat. 56 (1992), no. 2, 398--426; translation in Russian Acad. Sci. Izv. Math. 40 (1993), no. 2, 377--403 MR1180379 (93m:60119)

    Krylov, N. V. Quasiderivatives for solutions of Itô's stochastic equations and their applications. Stochastic analysis and related topics (Oslo, 1992), 1--44, Stochastics Monogr., 8, Gordon and Breach, Montreux, 1993. MR1268004 (95e:60057)

    Krylov, Nicolai V. Adapting some ideas from stochastic control theory to studying the heat equation in closed smooth domains. Special issue dedicated to the memory of Jacques-Louis Lions. Appl. Math. Optim. 46 (2002), no. 2-3, 231--261. MR1944761 (2003k:35085)

    Lieberman, Gary M. Second order parabolic differential equations. World Scientific Publishing Co., Inc., River Edge, NJ, 1996. xii+439 pp. ISBN: 981-02-2883-X MR1465184 (98k:35003)

    Oleui nik, O. A.; Radkeviv c, E. V. Second order equations with nonnegative characteristic form. (Russian) Mathematical analysis, 1969 (Russian), pp. 7--252. (errata insert) Akad. Nauk SSSR Vsesojuzn. Inst. Nauv cn. i Tehn. Informacii, Moscow, 1971. MR0457907(56 #16111); translation in Plenum Press, New York-London, 1973. vii+259 pp. ISBN: 0-306-30751-0 MR0457908(56 #16112)

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