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 50 条

[1] Gradient Estimates for Solutions to Divergence Form Elliptic Equations with Discontinuous Coefficients
Yan Yan Li
Michael Vogelius
Archive for Rational Mechanics and Analysis, 2000, 153 : 91 - 151
[2] Gradient estimates for parabolic problems with Orlicz growth and discontinuous coefficients
Oh, Jehan
Ok, Jihoon
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (14) : 8718 - 8736
[3] Gradient estimates in generalized Morrey spaces for parabolic operators
Byun, Sun-Sig
Softova, Lubomira G.
MATHEMATISCHE NACHRICHTEN, 2015, 288 (14-15) : 1602 - 1614
[4] Gradient estimates for divergence form parabolic systems from compositematerials
Dong, Hongjie
Xu, Longjuan
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2021, 60 (03)
[5] Morrey Estimates for Nondivergence Parabolic Operators with Discontinuous Coefficients on Homogeneous Groups
Tang Sufang
Wei Na
JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS, 2010, 23 (01): : 1 - 15
[6] On Probabilistic Analytical and Numerical Approaches for Divergence Form Operators with Discontinuous Coefficients
Talay, Denis
ADVANCES IN NUMERICAL SIMULATION IN PHYSICS AND ENGINEERING, 2014, 3 : 267 - 296
[7] Gradient Estimates for Elliptic Operators with Second-Order Discontinuous Coefficients
G. Metafune
L. Negro
C. Spina
Mediterranean Journal of Mathematics, 2019, 16
[8] Gradient Estimates for Elliptic Operators with Second-Order Discontinuous Coefficients
Metafunee, G.
Negro, L.
Spina, C.
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019, 16 (06)
[9] Gradient estimates for divergence form parabolic systems from composite materials
Hongjie Dong
Longjuan Xu
Calculus of Variations and Partial Differential Equations, 2021, 60
[10] L(p) estimates for divergence form elliptic equations with discontinuous coefficients.
DiFazio, G
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1996, 10A (02): : 409 - 420

← 1 2 3 4 5 →