论文标题
半线性椭圆方程及其应用的自由边界问题
A free boundary problem for semi-linear elliptic equation and its applications
论文作者
论文摘要
在本文中，我们考虑了具有Bernoulli类型自由边界的半连接椭圆方程的自由边界问题。解决方案对自由边界问题的存在和规律性是通过使用变分方法确定的。特别是，我们建立了最低限度的Lipschitz连续性和非分类性，以及自由边界的规律性。作为一种直接和重要的应用，本文还获得了稳定，不可压缩的无粘性射流和具有一般涡度的空洞流的结果。
In this paper, we consider a free boundary problem of a semilinear nonhomogeneous elliptic equation with Bernoulli's type free boundary. The existence and regularity of the solution to the free boundary problem are established by use of the variational approach. In particular, we establish the Lipschitz continuity and non-degeneracy of a minimum, and regularity of the free boundary. As a direct and important application, the well-posedness results on the steady, incompressible inviscid jet and cavitational flow with general vorticity are also obtained in this paper.
