Global regularity for higher order divergence elliptic and parabolic equations

被引：10

作者：

Wang, Lihe ^{[1
,2
]}

Yao, Fengping ^{[3
]}

机构：

[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[2] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

[3] Shanghai Univ, Dept Math, Shanghai 200436, Peoples R China

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2014年 / 266卷 / 02期

关键词：

Regularity; Sobolev; Orlicz spaces; Higher order; Divergence; Elliptic; Parabolic; Small BMO; The whole space; ORLICZ SPACES; SYSTEMS; FORM; COEFFICIENTS; OPERATORS;

D O I：

10.1016/j.jfa.2013.10.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we obtain the global regularity estimates of the weak solutions in Sobolev spaces and Orlicz spaces for higher order elliptic and parabolic equations of divergence form with small BMO coefficients in the whole space. We only focus on the parabolic case while the corresponding result in the elliptic case can be obtained as a corollary. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：792 / 813

页数：22

共 50 条

[31] Square function estimates on layer potentials for higher-order elliptic equations [J].

Barton, Ariel ;

Hofmann, Steve ;

Mayboroda, Svitlana .

MATHEMATISCHE NACHRICHTEN, 2017, 290 (16) :2459-2511

[32] Elliptic solutions for higher order KdV equations [J].

Hayashi, Masahito ;

Shigemoto, Kazuyasu ;

Tsukioka, Takuya .

JOURNAL OF PHYSICS COMMUNICATIONS, 2020, 4 (04)

[33] Second order regularity for solutions to anisotropic degenerate elliptic equations [J].

Baratta, Daniel ;

Muglia, Luigi ;

Vuono, Domenico .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2025, 435

[34] A regularity result for a class of elliptic equations with lower order terms [J].

Capone, Claudia ;

Radice, Teresa .

JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS, 2020, 6 (02) :751-771

[35] Zvonkin's transform and the regularity of solutions to double divergence form elliptic equations [J].

Bogachev, Vladimir I. ;

Rockner, Michael ;

Shaposhnikov, Stanislav V. .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2023, 48 (01) :119-149

[36] A regularity result for nonuniformly elliptic equations with lower order terms [J].

Radice, Teresa .

STUDIA MATHEMATICA, 2024, 276 (01) :1-17

[37] Nontangential Estimates on Layer Potentials and the Neumann Problem for Higher-Order Elliptic Equations [J].

Barton, Ariel ;

Hofmann, Steve ;

Mayboroda, Svitlana .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2021, 2021 (23) :18300-18366

[38] Global regularity in Orlicz-Morrey spaces of solutions to parabolic equations with VMO coefficients [J].

Guliyev, Vagif ;

Ekincioglu, Ismail ;

Ahmadli, Aysel ;

Omarova, Mehriban .

JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 2020, 11 (04) :1963-1989

[39] Optimal regularity estimates for parabolic p-harmonic equations [J].

Yao, Fengping .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 364 (02) :576-590

[40] HIGHER-ORDER REGULARITY FOR THE SOLUTIONS OF SOME DEGENERATE QUASI-LINEAR ELLIPTIC-EQUATIONS IN THE PLANE [J].

LIU, WB ;

BARRETT, JW .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1993, 24 (06) :1522-1536

← 1 2 3 4 5 →