On a class of elliptic free boundary problems with multiple solutions
Analysis of PDEs
2020-03-13 v1
Abstract
We prove that a certain class of elliptic free boundary problems, which includes the Prandtl-Batchelor problem from fluid dynamics as a special case, has two distinct nontrivial solutions for large values of a parameter. The first solution is a global minimizer of the energy. The energy functional is nondifferentiable, so standard variational arguments cannot be used directly to obtain a second nontrivial solution. We obtain our second solution as the limit of mountain pass points of a sequence of -functionals approximating the energy. We use careful estimates of the corresponding energy levels to show that this limit is neither trivial nor a minimizer.
Cite
@article{arxiv.2003.05921,
title = {On a class of elliptic free boundary problems with multiple solutions},
author = {Kanishka Perera},
journal= {arXiv preprint arXiv:2003.05921},
year = {2020}
}