低于临界增长 p -调和型方程组的完全正则性

数学物理学报

低于临界增长 p -调和型方程组的完全正则性

郑神州;赵书乐

北京交通大学数学系北京 100044

收稿日期:2005-12-08 修回日期:2007-09-20 出版日期:2008-06-25 发布日期:2008-06-25
通讯作者: 郑神州
基金资助:
北京交通大学``十五''专项基金(2004SM056)和国家自然科学基金(10671022)资助

Full Regularity of {\boldmath $p$}-Harmonic Type Systems Below

the Critical Growth

Zheng Shenzhou;Zhao Shule

Department of Mathematics, Beijing Jiaotong University, Beijing 100044

Received:2005-12-08 Revised:2007-09-20 Online:2008-06-25 Published:2008-06-25
Contact: Zheng Shenzhou

摘要/Abstract

摘要： 当p≥ 2时,得到一类低于临界增长的退化椭圆型方程组弱解微商属于局部Morrey-Campanauo空间$L^{ p,\lambda}$和${\cal L}^{p, \gamma}$;在附加条件下,
进一步建立其弱解微商的局部H\"older连续性.

关键词: Morrey-Campanato空间, p -调和方程组, 完全正则性

Abstract: For $p\geq 2$, the authors establish that each weak solution of a class of degenerate elliptic systems below the critical growth belongs to Morrey spaces. Furthermore, the authors obtain that the first derivative of each weak solution is locally H\"older continuous under additional conditions.

Key words: Morrey-Campanato spaces, $p$-Harmonic systems, Fully regularity

中图分类号:

45E05

郑神州;赵书乐. 低于临界增长 p -调和型方程组的完全正则性[J]. 数学物理学报, 2008, 28(3): 480-488.

Zheng Shenzhou;Zhao Shule.

Full Regularity of {\boldmath $p$}-Harmonic Type Systems Below

the Critical Growth

[J]. Acta mathematica scientia,Series A, 2008, 28(3): 480-488.

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