Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case
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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.
CitationWeiss, G. S. (2004). Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case. Electronic Journal of Differential Equations, 2004(44), pp. 1-12.
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