A free boundary problem for semi-linear elliptic equation and its applications
Analysis of PDEs
2020-06-04 v1
Abstract
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.
Cite
@article{arxiv.2006.02269,
title = {A free boundary problem for semi-linear elliptic equation and its applications},
author = {Jianfeng Cheng and Lili Du},
journal= {arXiv preprint arXiv:2006.02269},
year = {2020}
}
Comments
79 Pages, 11 figures. Any comments are welcome