Solvability of free boundary problems for steady groundwater flow
A. Yu. Beliaev · European Journal of Applied Mathematics · 2015
In this paper the free boundary problem for groundwater phreatic surface is represented in the form of a variational principle. It is proved that the flow domain Ω that solves the problem is a minimizer of some functional Λ(Ω). Weak solutions are introduced as minimizers of the lower semi-continuous regularization of Λ(⋅). Within this approach the existence of weak solutions is proved for a wide class of input data.