Regularity in free boundary problems
A free boundary value problem in potential theory
This paper is devoted to the formulation and solution of a free boundary problem for the Poisson equation in the plane. The object is to seek a domain and a function defined in satisfying the given differential equation together with both Dirichlet and Neumann type data on the boundary of . The Neumann data are given in a manner which permits reformulation of the problem as a variational inequality. Under suitable hypotheses about the given data, it is shown that there exists a unique solution...
Regularity in elliptic free boundary problems. II. Equations of higher order
Stable defects of minimizers of constrained variational principles
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