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

Electronic Journal of Differential Equations

关键词: Free boundary;    boundary regularity;    non-tangential touch;    monotonicity formula;    global regularity;    Bernoulli-type free boundary condition.;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown