English

The structure of finite Morse index solutions to two free boundary problems in $\mathbb{R}^2$

Analysis of PDEs 2017-12-05 v3

Abstract

We give a description of the structure of finite Morse index solutions to two free boundary problems in R2\mathbb{R}^2. These free boundary problems are models of phase transition and they are closely related to minimal hypersurfaces. We show that these finite Morse index solutions have finitely many ends and they converge exponentially to these ends at infinity. As an important tool in the proof, a quadratic decay estimate for the curvature of free boundaries is established.

Keywords

Cite

@article{arxiv.1506.00491,
  title  = {The structure of finite Morse index solutions to two free boundary problems in $\mathbb{R}^2$},
  author = {Kelei Wang},
  journal= {arXiv preprint arXiv:1506.00491},
  year   = {2017}
}