Regularity of Weak Solutions of Nonlinear Equations with Discontinuous Coefficients

被引：0

作者：

Qi Kang RAN Department of Applied Mathematics

机构：

来源：

Acta Mathematica Sinica,English Series | 2005年 / 21卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Nonlinear elliptic equations; Local Regularity; Calderón-Zygmund decomposition; VMO space; Local weak L~p(Ω) space;

D O I：

暂无

中图分类号：

O241.7 [非线性代数方程和超越方程的数值解法];

学科分类号：

070102 ;

摘要：

In this paper,we prove that the weak solutions u∈W(Ω) (1<p≥∞) of the followingequation with vanishing mean oscillation coefficients A(x):-div[(A(x)▽u·▽u)~((p-2)/2)A(x)▽u+|F(x)|F(x)]=B(x,u,▽u)belong to W(Ω) ( q∈(p,∞)),provided F∈L~q(Ω) and B(x,u,h) satisfies proper growth con-ditions,where Ω R~N (N 2) is a bounded open set,A(x)=(A(x))is a symmetric matrixfunction.

引用

页码：705 / 714

页数：10

共 50 条

[1] Regularity of weak solutions of nonlinear equations with discontinuous coefficients
Ran, QK
[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2005, 21 (04) : 705 - 714
[2] Regularity of Weak Solutions of Nonlinear Equations with Discontinuous Coefficients
Qi Kang Ran
[J]. Acta Mathematica Sinica, 2005, 21 : 705 - 714
[3] Interior regularity for weak solutions of ultraparabolic equations in divergence form with discontinuous coefficients.
Manfredini, M
Polidoro, S
[J]. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1998, 1B (03): : 651 - 675
[4] Weak Solutions of Stochastic Differential Equations with Discontinuous Coefficients
A. A. Levakov
[J]. Differential Equations, 2001, 37 : 1088 - 1096
[5] Weak solutions of stochastic differential equations with discontinuous coefficients
Levakov, AA
[J]. DIFFERENTIAL EQUATIONS, 2001, 37 (08) : 1088 - 1096
[6] On regularity and existence of weak solutions to nonlinear Kolmogorov-Fokker-Planck type equations with rough coefficients
Garain, Prashanta
Nystrom, Kaj
[J]. MATHEMATICS IN ENGINEERING, 2023, 5 (02): : 1 - 37
[7] REGULARITY OF BOUNDED WEAK-SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS
TODOROV, TG
[J]. VESTNIK LENINGRADSKOGO UNIVERSITETA SERIYA MATEMATIKA MEKHANIKA ASTRONOMIYA, 1975, (04): : 56 - 63
[8] Interior W1,p Regularity and Holder Continuity of Weak Solutions to a Class of Divergence Kolmogorov Equations with Discontinuous Coefficients
Zhu, Maochun
Niu, Pengcheng
[J]. MILAN JOURNAL OF MATHEMATICS, 2013, 81 (02) : 317 - 346
[9] Partial regularity for weak solutions of nonlinear elliptic equations with supercritical exponents
Hou, SB
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 59 (07) : 1045 - 1061
[10] HIGHER REGULARITY OF WEAK SOLUTIONS OF STRONGLY NONLINEAR ELLIPTIC-EQUATIONS
SIMADER, CG
[J]. LECTURE NOTES IN MATHEMATICS, 1986, 1192 : 243 - 246

← 1 2 3 4 5 →