数学物理学报(英文版) ›› 1993, Vol. 13 ›› Issue (3): 266-272.

• 论文 • 上一篇    下一篇

ON THE REGULARITY OF THE MINIMUM SOLUTION OF THE RESTRAINED VARIATIONAL PROBLEMS

沈尧天1, 郭信康2   

  1. 1. Dept. of Appl. Math., South China Univ. of Tech., Guangzhou 510641, China;
    2. Inst. of Math., Guangxi Univ., Nanning 530004, China
  • 收稿日期:1989-04-14 出版日期:1993-09-25 发布日期:1993-09-25

ON THE REGULARITY OF THE MINIMUM SOLUTION OF THE RESTRAINED VARIATIONAL PROBLEMS

Shen Yaotian1, Guo Xinkang2   

  1. 1. Dept. of Appl. Math., South China Univ. of Tech., Guangzhou 510641, China;
    2. Inst. of Math., Guangxi Univ., Nanning 530004, China
  • Received:1989-04-14 Online:1993-09-25 Published:1993-09-25

摘要: This paper is concerned with the regularity of minimum solution u of the following functional
L(u)=∫0aαβ(x)gij(u)DauiDβvidx
on the restraint E={uW01,2(Ω,RN)||u|Lp=1}Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Hölder continuous.

Abstract: This paper is concerned with the regularity of minimum solution u of the following functional
L(u)=∫0aαβ(x)gij(u)DauiDβvidx
on the restraint E={uW01,2(Ω,RN)||u|Lp=1}Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Hölder continuous.