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Some $L_{p}$-estimates for elliptic and parabolic operators with measurable coefficients
1. | 127 Vincent Hall, University of Minnesota, Minneapolis, MN 55455, United States |
References:
[1] |
Hongjie Dong, N. V. Krylov and Xu Li, On fully nonlinear elliptic and parabolic equations in domains with VMO coefficients, Algebra i Analiz, Vol. 24 (2012), No. 1, 54-95. |
[2] |
N. V. Krylov, On Itô's stochastic integral equations, (Russian), Teoriya Veroyatnostei i eye Primeneniya, 14 (1969), 340-348; English translation in Theor. Probability Appl., 14 (1969), 330-336. |
[3] |
N. V. Krylov, Certain estimates in the theory of stochastic integrals, (Russian), Teoriya Veroyatnostei i eye Primeneniya, 18 (1973), 56-65; English translation in Theor. Probability Appl., 18 (1973), 54-63. |
[4] |
N. V. Krylov, Some estimates for the density of the distrinbution of a stochastic integral, (Russian), Izvestiya Akademii Nauk SSSR, seriya matematicheskaya, 38 (1974), 228-248; English translation in Math. USSR Izvestija, 8 (1974), 233-254. |
[5] |
N. V. Krylov, "Controlled Diffusion Processes,'' (Russian), Nauka, Moscow, 1977; English translation, Applications of Mathematics, 14, Springer-Verlag, New York-Berlin, 1980. |
[6] |
N. V. Krylov, "Nelineĭnye Éllipticheskie i Parabolicheskie Uravneniya Vtorogo Poryadka,'' (Russian) [Second-Order Nonlinear Elliptic and Parabolic Equations], "Nauka," Moscow, 1985; English translation, Reidel, Dordrecht, 1987, MR0901759. |
[7] |
N. V. Krylov, "Lectures on Elliptic and Parabolic Equations in Sobolev Spaces," Graduate Studies in Mathematics, 96, Amer. Math. Soc., Providence, RI, 2008. |
[8] |
N. V. Krylov, On Bellman's equations with VMO coefficients, Methods and Applications of Analysis, 17 (2010), 105-121. |
[9] |
Fang-Hua Lin, Second derivative $L^p$-estimates for elliptic equations of nondivergent type, Proc. Amer. Math. Soc., 96 (1986), 447-451.
doi: 10.2307/2046592. |
[10] |
O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'tseva, "Lineĭnye i Kvazilineĭnye Uravneniya Parabolicheskogo Tipa,'' (Russian) [Linear and Quasi-Linear Equations of Parabolic Type], "Nauka," Moscow, 1968; English translation, Amer. Math. Soc., Providence, RI, 1968. |
[11] |
G. M. Lieberman, "Second Order Parabolic Differential Equations," World Scientific Publishing Co., Inc., River Edge, NJ, 1996. |
show all references
References:
[1] |
Hongjie Dong, N. V. Krylov and Xu Li, On fully nonlinear elliptic and parabolic equations in domains with VMO coefficients, Algebra i Analiz, Vol. 24 (2012), No. 1, 54-95. |
[2] |
N. V. Krylov, On Itô's stochastic integral equations, (Russian), Teoriya Veroyatnostei i eye Primeneniya, 14 (1969), 340-348; English translation in Theor. Probability Appl., 14 (1969), 330-336. |
[3] |
N. V. Krylov, Certain estimates in the theory of stochastic integrals, (Russian), Teoriya Veroyatnostei i eye Primeneniya, 18 (1973), 56-65; English translation in Theor. Probability Appl., 18 (1973), 54-63. |
[4] |
N. V. Krylov, Some estimates for the density of the distrinbution of a stochastic integral, (Russian), Izvestiya Akademii Nauk SSSR, seriya matematicheskaya, 38 (1974), 228-248; English translation in Math. USSR Izvestija, 8 (1974), 233-254. |
[5] |
N. V. Krylov, "Controlled Diffusion Processes,'' (Russian), Nauka, Moscow, 1977; English translation, Applications of Mathematics, 14, Springer-Verlag, New York-Berlin, 1980. |
[6] |
N. V. Krylov, "Nelineĭnye Éllipticheskie i Parabolicheskie Uravneniya Vtorogo Poryadka,'' (Russian) [Second-Order Nonlinear Elliptic and Parabolic Equations], "Nauka," Moscow, 1985; English translation, Reidel, Dordrecht, 1987, MR0901759. |
[7] |
N. V. Krylov, "Lectures on Elliptic and Parabolic Equations in Sobolev Spaces," Graduate Studies in Mathematics, 96, Amer. Math. Soc., Providence, RI, 2008. |
[8] |
N. V. Krylov, On Bellman's equations with VMO coefficients, Methods and Applications of Analysis, 17 (2010), 105-121. |
[9] |
Fang-Hua Lin, Second derivative $L^p$-estimates for elliptic equations of nondivergent type, Proc. Amer. Math. Soc., 96 (1986), 447-451.
doi: 10.2307/2046592. |
[10] |
O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'tseva, "Lineĭnye i Kvazilineĭnye Uravneniya Parabolicheskogo Tipa,'' (Russian) [Linear and Quasi-Linear Equations of Parabolic Type], "Nauka," Moscow, 1968; English translation, Amer. Math. Soc., Providence, RI, 1968. |
[11] |
G. M. Lieberman, "Second Order Parabolic Differential Equations," World Scientific Publishing Co., Inc., River Edge, NJ, 1996. |
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