论文标题
二维方程的解决方案的凹入度二维方程式
Concavity of solutions to semilinear equations in dimension two
论文作者
论文摘要
我们考虑了在二维凸域上的一类半线性方程的差异问题。我们给出了足够的条件，使溶液具有凹形。我们的病情使用椭圆的比较，并由Kosmodem'yanskii的想法进行。 我们还证明了从边界繁殖解决方案的凹入性的结果，这在各个方面都具有。
We consider the Dirichlet problem for a class of semilinear equations on two dimensional convex domains. We give a sufficient condition for the solution to be concave. Our condition uses comparison with ellipses, and is motivated by an idea of Kosmodem'yanskii. We also prove a result on propagation of concavity of solutions from the boundary, which holds in all dimensions.
