Parabolic and elliptic equations with VMO coefficients

被引：218
作者：
Krylov, N. V. [1 ]
机构：
[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA
来源：
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2007年 / 32卷 / 03期
基金：
美国国家科学基金会;
关键词：
martingale problem; second-order equations; vanishing mean oscillation;
D O I：
10.1080/03605300600781626
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An L-p-theory of divergence and non-divergence form elliptic and parabolic equations is presented. The main coefficients are supposed to belong to the class VMOx, which, in particular, contains all functions independent of x. Weak uniqueness of the martingale problem associated with such equations is obtained.
引用
收藏
页码：453 / 475
页数：23
相关论文
共 17 条
[1]  
[Anonymous], 1996, GRADUATE STUDIES MAT
[2]  
[Anonymous], 1972, ANN SCUOLA NORM-SCI
[3]   W(P)(1,2) SOLVABILITY FOR THE CAUCHY-DIRICHLET PROBLEM FOR PARABOLIC EQUATIONS WITH VMO COEFFICIENTS [J].
BRAMANTI, M ;
CERUTTI, MC .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1993, 18 (9-10) :1735-1763
[4]   Parabolic equations with BMO coefficients in Lipschitz domains [J].
Byun, SS .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 209 (02) :229-265
[5]   Elliptic equations with BMO coefficients in Lipschitz domains [J].
Byun, SS .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 357 (03) :1025-1046
[6]   W2,P-SOLVABILITY OF THE DIRICHLET PROBLEM FOR NONDIVERGENCE ELLIPTIC-EQUATIONS WITH VMO COEFFICIENTS [J].
CHIARENZA, F ;
FRASCA, M ;
LONGO, P .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 336 (02) :841-853
[7]  
Chiarenza F., 1991, Ricerche Mat, V40, P149
[8]  
Denk R, 2003, MEM AM MATH SOC, V166, P1
[9]   Lp-Lq estimates for parabolic systems in non-divergence form with VMO coefficients [J].
Haller-Dintelmann, Robert ;
Heck, Horst ;
Hieber, Matthias .
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2006, 74 :717-736
[10]  
KIM D, UNPUB POTENTIAL ANAL
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