Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 44, pp. 1-12.

Title: Boundary monotonicity formulae and applications to 
       free boundary problems I: The elliptic case
       
Author: Georg S. Weiss (Univ. of Tokyo, Japan)

Abstract: 
 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.
  
Submitted October 13, 2003. Published March 29, 2004.
Math Subject Classifications: 35R35, 35J67, 35J60.
Key Words: Free boundary; boundary regularity; non-tangential touch; 
           monotonicity formula; global regularity;
           Bernoulli-type free boundary condition.