Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case

Date

2004-03-29

Authors

Weiss, Georg S.

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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.

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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.

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Attribution 4.0 International

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