%0 Journal Article
%T Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case
%A Georg S. Weiss
%J Electronic Journal of Differential Equations
%D 2004
%I Texas State University
%X We derive a monotonicity formula at boundary points for a class of nonlinear elliptic partial differential equations, including the obstacle problem case, quenching, a free boundary problem with Bernoulli-type free boundary condition as well as the blow-up case. As application model we prove - for Dirichlet boundary data satisfying certain assumptions - the global existence of a classical solution of the free boundary problem with Bernoulli-type free boundary condition in two and three dimensions.
%K Free boundary
%K boundary regularity
%K non-tangential touch
%K monotonicity formula
%K global regularity
%K Bernoulli-type free boundary condition.
%U http://ejde.math.txstate.edu/Volumes/2004/44/abstr.html