Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case
Date
2004-03-29
Authors
Weiss, Georg S.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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.
Description
Keywords
Free boundary, Boundary regularity, Non-tangential touch, Monotonicity formula, Global regularity, Bernoulli-type free boundary condition
Citation
Weiss, G. S. (2004). Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case. <i>Electronic Journal of Differential Equations, 2004</i>(44), pp. 1-12.
Rights
Attribution 4.0 International