论文标题
一阶段无边界问题的图形解决方案
Graphical solutions to one-phase free boundary problems
论文作者
论文摘要
我们研究了经典的一相问题及其薄的粘度解决方案。在低维度中，我们表明，当自由边界是连续函数的图时，解决方案是半平面解。在显着的维度上，这回答了伯恩斯坦问题最小表面问题的单相自由边界类似物。 作为应用程序，我们还将半线性方程的单调溶液与凸起类型的非线性进行了分类。
We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when the free boundary is the graph of a continuous function, the solution is the half-plane solution. This answers, in the salient dimensions, a one-phase free boundary analogue of Bernstein's problem for minimal surfaces. As an application, we also classify monotone solutions of semilinear equations with a bump-type nonlinearity.
