论文标题
边界附近的椭圆形半线性方程的大量解决方案
Large solutions of elliptic semilinear equations non-degenerate near the boundary
论文作者
论文摘要
在本文中，我们研究了带有非零源项的所谓椭圆形半线性方程的大型解决方案，因此，在域的边界上爆炸的溶液在域的边界上吹来，因为它们在弱最大原理持有时都大于任何其他解决方案。关于大型解决方案的主要主题是独特结果及其在边界附近的行为。它远不远胜于简单。所考虑的半线性方程的结构包括众所周知的凯勒 - 塞尔曼积分和对差异操作员领先部分椭圆度的假设。在我们的研究中，需要在边界附近一个均匀的椭圆度。我们考虑了PDE中的源术语，其边界爆炸与Keller-Sosserman条件一致。还研究了该来源上的额外的凯勒 - 塞尔曼爆炸，特别是在某些情况下，PDE仅接受大型解决方案。
In this paper we study the so-called large solutions of elliptic semilinear equations with non null sources term, thus solutions blowing up on the boundary of the domain for which reason they are greater than any other solution whenever Weak Maximum Principle holds. The main topic about large solutions is uniqueness results and their behavior near the boundary. It is much less than being simple. The structure of the semilinear equations considered includes the well known Keller-Osserman integral and an assumption on the ellipticity of the leading part of the differential operator. In our study an uniform ellipticity near the boundary is required. We consider source terms in the PDE whose boundary explosion is consistent with the Keller-Osserman condition. Extra Keller-Osserman explosions on the source are also studied, showing in particular that in some cases the PDE only admits large solutions.
