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Wω2,p -Solvability of the Cauchy–Dirichlet Problem for Nondivergence Parabolic Equations with BMO Coefficients

Published online by Cambridge University Press:  20 November 2018

Lin Tang*
Affiliation:
LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, P.R. China email: [email protected]
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Abstract

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In this paper, we establish the regularity of strong solutions to nondivergence parabolic equations with BMO coefficients in nondoubling weighted spaces.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2012

References

[1] Acquistapace, P., On BMO regularity for linear elliptic systems. Ann. Mat. Pura Appl. 161(1992), 231-269. http://dx. doi. org/10.1007/BF01759640Google Scholar
[2] Alvarez, J., Bagby, R., Kurtz, D., and Pérez, C., Weighted estimates for commutators of linear operator. Studia Math. 104(1993), no. 2, 195-209.Google Scholar
[3] Byun, S.-S., Parabolic equations with BMO coefficients in Lipschitz domains. J. Differential Equations 209(2005), no. 2, 229-265. http://dx. doi. org/10.1016/j. jde.2004.08.018Google Scholar
[4] Bramanti, M. and Cerutti, M.,W1,2 p solvability for the Cauchy-Dirichlet problem for parabolic equations with VMO coefficients. Comm. Partial Differential Equations 18(1993), no. 9-10, 1735-1763. http://dx. doi. org/10.1080/03605309308820991Google Scholar
[5] Chiarenza, F., Frasca, M., and Longo, P., Interior W 2, p estimates for nondivergence elliptic equations with discontinuous coefficients. Ricerche. Mat. 40(1991), no. 1, 149-168.Google Scholar
[6] Chiarenza, F., Frasca, M., and Longo, P.,W2,p solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients. Trans. Amer. Math. Soc. 336(1993), no. 2, 841-853. http://dx. doi. org/10.2307/2154379Google Scholar
[7] Haller-Dintelmann, R., Heck, H., and Hieber, M., LpLq estimates for parabolic systems in non-divergence form with VMO coefficients. J. London Math. Soc. 74(2006), no. 3, 717-736. http://dx. doi. org/10.1112/S0024610706023192Google Scholar
[8] Fabe, E. and Riviere, N., Symbolic calculus of kernels with mixed homogeneity. In: Singular Integrals. American Mathematical Society, Providence, RI, 1967, pp. 106-127.Google Scholar
[9] Garćıa-Cuerva, J. and Rubio de Francia, J., Weighted Norm Inequalities nnd Related Topics. North-Holland Mathematics Studies 116, North-Holland, Amsterdam, 1985.Google Scholar
[10] Heck, H. and Hieber, M., Maximal Lp-regularity for elliptic operators with VMO-coefficients. J. Evol. Equ. 3(2003), no. 2, 332-359.Google Scholar
[11] Jones, P., Extension theorems for BMO. Indiana Univ. Math. J. 29(1980), no. 1, 41-66. http://dx. doi. org/10.1512/iumj.1980.29.29005Google Scholar
[12] John, F. and Nirenberg, L., On functions of bounded mean oscillation. Comm. Pure Appl. Math, 14(1961), 415-426. http://dx. doi. org/10.1002/cpa.3160140317Google Scholar
[13] Li, X. and Yang, D., Boundedness of some sublinear operators on Herz spaces. Illinois J. Math. 40(1996), no. 3, 494-501.Google Scholar
[14] Krylov, N., Parabolic and elliptic equations with VMO coefficients. Comm. Partial Differential Equations 32(2007), no. 1-3, 453-475. http://dx. doi. org/10.1080/03605300600781626Google Scholar
[15] Krylov, N., Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms. J. Funct. Anal. 250(2007), no. 2, 521-558. http://dx. doi. org/10.1016/j. jfa.2007.04.003Google Scholar
[16] Krylov, N., Lectures on Elliptic and Parabolic Equations in Sobolev spaces. Graduate Studies in Mathematics 96. American Mathematical Society, Providence, RI, 2008.Google Scholar
[17] Krylov, N., On parabolic PDEs and SPDEs in Sobolev spaces W 2,p without and with weights. In: Topics in Stochastic Analysis and Nonparametric Estimation. IMA Vol. Math. Appl. 145, Springer, New York, 2008, pp. 151-197.Google Scholar
[18] Sarason, D., Functions of vanishing mean oscillation. Trans. Amer. Math. Soc. 207(1975), 391-405. http://dx. doi. org/10.1090/S0002-9947-1975-0377518-3Google Scholar