论文标题
飞机中自由边界问题的全球解决方案的分类
Classification of global solutions of a free boundary problem in the plane
论文作者
论文摘要
我们对方程式\ begin {equation*}Δu=γu^{γ-1} \ end end {equation*}的非平地，非负，均匀的均质解分类。 该问题是由对经典Alt-Phillips自由边界问题的分析所激发的，但在这里考虑了负指数$γ$。 证明依赖于普通微分方程的几个定制结果。
We classify nontrivial, nonnegative, positively homogeneous solutions of the equation \begin{equation*} Δu=γu^{γ-1} \end{equation*} in the plane. The problem is motivated by the analysis of the classical Alt-Phillips free boundary problem, but considered here with negative exponents $γ$. The proof relies on several bespoke results for ordinary differential equations.
