Title

On a class of elliptic free boundary problems with multiple solutions

Authors

Kanishka Perera

Document Type

Article

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 C1-functionals approximating the energy. We use careful estimates of the corresponding energy levels to show that this limit is neither trivial nor a minimizer.

Publication Date

3-2020

Comments

http://hdl.handle.net/11141/3378

Recommended Citation

Perera, Kanishka, "On a class of elliptic free boundary problems with multiple solutions" (2020). Mathematics and System Engineering Faculty Publications. 99.
https://repository.fit.edu/math_faculty/99