Weiss, Georg S.2021-04-132021-04-132004-03-29Weiss, 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. 1-12.1072-6691https://hdl.handle.net/10877/13372We 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.Text12 pages1 file (.pdf)enAttribution 4.0 InternationalFree boundaryBoundary regularityNon-tangential touchMonotonicity formulaGlobal regularityBernoulli-type free boundary conditionArticle