REGULARITY OF H1 ∩Ln((γ-1)/(2-γ)) WEAK SOLUTIONS FOR NONLINEAR ELLIPTIC SYSTEMS

数学物理学报(英文版) ›› 1990, Vol. 10 ›› Issue (2): 173-184.

REGULARITY OF H¹ ∩L^{n((γ-1)/(2-γ))} WEAK SOLUTIONS FOR NONLINEAR ELLIPTIC SYSTEMS

何旭东, 陈宝耀

Dept. of Math., Zhongshan Univ., Guangzhou, China

收稿日期:1988-05-16 修回日期:1988-12-26 出版日期:1990-06-25 发布日期:1990-06-25
基金资助:
This work is supported in part by the Foundation of Zhongshan University, Advanced Research Center.

REGULARITY OF H¹ ∩L^{n((γ-1)/(2-γ))} WEAK SOLUTIONS FOR NONLINEAR ELLIPTIC SYSTEMS

He Xudong, Chen Baoyao

Dept. of Math., Zhongshan Univ., Guangzhou, China

Received:1988-05-16 Revised:1988-12-26 Online:1990-06-25 Published:1990-06-25
Supported by:
This work is supported in part by the Foundation of Zhongshan University, Advanced Research Center.

摘要/Abstract

摘要： Let us consider the following elliptic systems of second order
-D_α(A_i^α(x, u, Du))=B_i(x, u, Du), i=1, …, N, x∈Ω⊂Rⁿ, n ≥ 3 (1) and suppose
ⅰ)|A_i^α(x, u, Du)| ≤ L(1+|Du|);
ⅱ) (1+|p|)^-1 A_i^α(x, u, p)are Hölder-continuous functions with some exponent δ on Ω×R^N uniformly with respect to p, i.e.

何旭东, 陈宝耀. REGULARITY OF H¹ ∩L^{n((γ-1)/(2-γ))} WEAK SOLUTIONS FOR NONLINEAR ELLIPTIC SYSTEMS[J]. 数学物理学报(英文版), 1990, 10(2): 173-184.

He Xudong, Chen Baoyao. REGULARITY OF H¹ ∩L^{n((γ-1)/(2-γ))} WEAK SOLUTIONS FOR NONLINEAR ELLIPTIC SYSTEMS[J]. Acta mathematica scientia,Series B, 1990, 10(2): 173-184.

REGULARITY OF H¹ ∩L^{n((γ-1)/(2-γ))} WEAK SOLUTIONS FOR NONLINEAR ELLIPTIC SYSTEMS

REGULARITY OF H¹ ∩L^{n((γ-1)/(2-γ))} WEAK SOLUTIONS FOR NONLINEAR ELLIPTIC SYSTEMS

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