BOUNDARY MONOTONICITY FORMULAE AND APPLICATIONS TO FREE BOUNDARY PROBLEMS I: THE ELLIPTIC CASE
BOUNDARY MONOTONICITY FORMULAE AND APPLICATIONS TO FREE BOUNDARY PROBLEMS I: THE ELLIPTIC CASE
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发表时间：
2004
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通讯作者：
G. Weiss
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作者：
G. Weiss
得到了一类非线性椭圆型偏微分方程在边界点处的单调性公式，包括障碍问题情形、熄灭情形、自由边界问题的Bernoulli型自由边界条件以及Blow-up情形.作为应用模型，我们证明了-Dirichlet边界数据满足一定的假设-在二维和三维的Bernoulli型自由边界条件的自由边界问题的经典解的整体存在性。
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.