Generalized Money estimates for the gradient of divergence form parabolic operators with discontinuous coefficients

被引：18

作者：

Guliyev, Vagif S. ^{[1
,2
]}

Softova, Lubomira G. ^{[3
]}

机构：

[1] Ahi Evran Univ, Dept Math, Kirsehir, Turkey

[2] Azerbaijan Acad Sci, Inst Math & Mech, AZ-1141 Baku, Azerbaijan

[3] Univ Naples 2, Dept Civil Engn Design Construct & Environm, Naples, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 259卷 / 06期

关键词：

Generalized Money spaces; Parabolic operators; Cauchy-Dirichlet problem; Measurable coefficients; BMO; Gradient estimates; SINGULAR INTEGRAL-OPERATORS; MORREY SPACES; MAXIMAL OPERATOR; BMO COEFFICIENTS; EQUATIONS; DOMAINS; BOUNDEDNESS; REGULARITY;

D O I：

10.1016/j.jde.2015.03.032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Cauchy Dirichlet problem for linear divergence form parabolic operators in bounded Reifenberg-flat domains. The coefficients are supposed to be only measurable in one of the space variables and small BMO with respect to the others. We obtain boundedness of the Hardy-Littlewood maximal operator in the generalized Morrey spaces W-rho,W-phi, p is an element of (1, infinity) and weight phi satisfying certain supremum condition. This permits us to obtain Calderon-Zygmund type estimate for the gradient of the weak solution of the problem. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：2368 / 2387

页数：20

共 42 条

[31] Generalized Vanishing Mean Oscillation Spaces Associated with Divergence Form Elliptic Operators [J].

Jiang, Renjin ;

Yang, Dachun .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2010, 67 (01) :123-149

[32] Unique continuation for the gradient of eigenfunctions and Wegner estimates for random divergence-type operators [J].

Dicke, Alexander ;

Veselic, Ivan .

JOURNAL OF FUNCTIONAL ANALYSIS, 2023, 285 (07)

[33] Generalized Vanishing Mean Oscillation Spaces Associated with Divergence Form Elliptic Operators [J].

Renjin Jiang ;

Dachun Yang .

Integral Equations and Operator Theory, 2010, 67 :123-149

[34] On local regularity estimates for fractional powers of parabolic operators with time-dependent measurable coefficients [J].

Litsgard, Malte ;

Nystroem, Kaj .

JOURNAL OF EVOLUTION EQUATIONS, 2023, 23 (01)

[35] Gradient Estimates for Commutators of Square Roots of Elliptic Operators with Complex Bounded Measurable Coefficients [J].

Chen, Yanping ;

Ding, Yong .

JOURNAL OF GEOMETRIC ANALYSIS, 2017, 27 (01) :466-491

[36] Global gradient estimates for divergence-type elliptic problems involving general nonlinear operators [J].

Cho, Yumi .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (10) :6152-6190

[37] INTERIOR LP ESTIMATES FOR DEGENERATE ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH V M O COEFFICIENTS [J].

Di Fazio, G. ;

Fanciullo, M. S. ;

Zamboni, P. .

DIFFERENTIAL AND INTEGRAL EQUATIONS, 2012, 25 (7-8) :619-628

[38] BMO ESTIMATES FOR NONVARIATIONAL OPERATORS WITH DISCONTINUOUS COEFFICIENTS STRUCTURED ON HORMANDER'S VECTOR FIELDS ON CARNOT, GROUPS [J].

Bramanti, Marco ;

Fanciullo, Maria Stella .

ADVANCES IN DIFFERENTIAL EQUATIONS, 2013, 18 (9-10) :955-1004

[39] Lq estimates for nonlocal p-Laplacian-type equations with BMO kernel coefficients in divergence form [J].

Byun, Sun-Sig ;

Kim, Kyeongbae .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2025, 27 (09)

[40] Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces (vol 14, pg 49, 2016) [J].

Guliyev, Vagif S. ;

Omarova, Mehriban N. .

OPEN MATHEMATICS, 2016, 14 :283-285

← 1 2 3 4 5 →