Optimal conditions for L∞-regularity and a priori estimates for semilinear elliptic systems
Optimal conditions for L∞-regularity and a priori estimates for semilinear elliptic systems
复制标题
DOI：
10.1016/j.jmaa.2008.10.013
复制
发表时间：
2009-03
影响因子：
1.3
通讯作者：
Yuxiang Li
中科院分区：
文献类型：
--
作者：
Yuxiang Li
在本文中，我们提出了具有n（小于或等于3）个分量的半线性椭圆系统的自举程序。结合lp - lq -估计，给出了h01 -解、l1 -解和Lδ1-解三种已知弱解的最优L∞-正则性条件。由于Lδp的线性理论（Ω），它也产生了l δ1解的先验估计的最佳条件。在先验估计的基础上，改进了若干类椭圆系统的已知存在性定理。
In this paper, we present a bootstrap procedure for semilinear elliptic systems with n (⩾3) components. Combining with the Lp–Lq-estimates, it yields the optimal L∞-regularity conditions for the three well known types of weak solutions: H01-solutions, L1-solutions and Lδ1-solutions. Thanks to the linear theory in Lδp(Ω), it also yields the optimal conditions for a priori estimates for Lδ1-solutions. Based on the a priori estimates, we improve known existence theorems for some classes of elliptic systems.