Gradient estimates in generalized Morrey spaces for parabolic operators

被引：15

作者：

Byun, Sun-Sig ^{[1
,2
]}

Softova, Lubomira G. ^{[3
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

[2] Seoul Natl Univ, Res Inst Math, Seoul 151747, South Korea

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

来源：

MATHEMATISCHE NACHRICHTEN | 2015年 / 288卷 / 14-15期

基金：

新加坡国家研究基金会;

关键词：

Generalized Morrey spaces; Parabolic equations and systems; Cauchy-Dirichlet problem; Measurable coefficients; BMO; Gradient estimates; REIFENBERG-FLAT DOMAINS; ELLIPTIC-EQUATIONS; SINGULAR-INTEGRALS; BMO COEFFICIENTS; DIVERGENCE FORM; REGULARITY;

D O I：

10.1002/mana.201400113

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain global regularity in generalized Morrey spaces for the gradient of the weak solutions to divergence form linear parabolic operators with measurable data. Assuming partial BMO smallness of the coefficients and Reifenberg flatness of the boundary of the underlying domain, we develop a Calderon-Zygmund type theory for such operators. Problems like the considered here arise in the modeling of composite materials and in the mechanics of membranes and films of simple nonhomogeneous materials which form a linear laminated medium. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：1602 / 1614

页数：13

共 50 条

[1] Gradient Estimates for Parabolic Equations in Generalized Weighted Morrey Spaces
Vagif GULIYEV
Shamsiyya MURADOVA
Mehriban OMAROVA
Lubomira SOFTOVA
[J]. Acta Mathematica Sinica,English Series, 2016, 32 (08) : 911 - 924
[2] Gradient Estimates for Parabolic Equations in Generalized Weighted Morrey Spaces
Vagif GULIYEV
Shamsiyya MURADOVA
Mehriban OMAROVA
Lubomira SOFTOVA
[J]. Acta Mathematica Sinica., 2016, 32 (08) - 924
[3] Gradient estimates for parabolic equations in generalized weighted Morrey spaces
Vagif Guliyev
Shamsiyya Muradova
Mehriban Omarova
Lubomira Softova
[J]. Acta Mathematica Sinica, English Series, 2016, 32 : 911 - 924
[4] Gradient estimates for parabolic equations in generalized weighted Morrey spaces
Guliyev, Vagif
Muradova, Shamsiyya
Omarova, Mehriban
Softova, Lubomira
[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2016, 32 (08) : 911 - 924
[5] Estimates in generalized Morrey spaces for linear parabolic systems
McBride, Matt
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 452 (02) : 1019 - 1030
[6] Estimates for parabolic equations with measure data in generalized Morrey spaces
Zhang, Chao
[J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2019, 21 (05)
[7] PARABOLIC FRACTIONAL INTEGRAL OPERATORS WITH ROUGH KERNEL IN PARABOLIC GENERALIZED MORREY SPACES
Guliyev, Vagif S.
Balakishiyev, Aydin S.
[J]. PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, 2013, 38 (46): : 47 - 56
[8] Gradient estimates of parabolic Cauchy–Dirichlet problems on Morrey–Banach spaces
Kwok-Pun Ho
[J]. Journal of Elliptic and Parabolic Equations, 2022, 8 : 743 - 766
[9] PARABOLIC FRACTIONAL MAXIMAL AND INTEGRAL OPERATORS WITH ROUGH KERNELS IN PARABOLIC GENERALIZED MORREY SPACES
Guliyev, Vagif S.
Balakishiyev, Aydin S.
[J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2015, 9 (01): : 257 - 276
[10] NORM ESTIMATES FOR BESSEL-RIESZ OPERATORS ON GENERALIZED MORREY SPACES
Idris, Mochammad
Gunawan, Hendra
Eridani
[J]. MATHEMATICA BOHEMICA, 2018, 143 (04): : 409 - 417

← 1 2 3 4 5 →