论文标题
无穷laplacian的反应扩散方程
Reaction-diffusion equations for the infinity Laplacian
论文作者
论文摘要
当右手侧没有改变符号并满足一定的生长条件时，我们为跨自由边界的不均匀无限拉普拉斯方程的粘度解决方案提供了尖锐的规律性。我们证明了解决方案的几何规律性估计，并得出结论，一旦源项与均匀函数相媲美，自由边界是多孔集合，因此具有零lebesgue度量。此外，我们得出了liouville型定理。当靠近起点时，右侧的增长速度不超过三级均匀功能，我们表明，如果非负粘度解决方案在某个点消失，那么它必须到处消失。
We derive sharp regularity for viscosity solutions of an inhomogeneous infinity Laplace equation across the free boundary, when the right hand side does not change sign and satisfies a certain growth condition. We prove geometric regularity estimates for solutions and conclude that once the source term is comparable to a homogeneous function, then the free boundary is a porous set and hence, has zero Lebesgue measure. Additionally, we derive a Liouville type theorem. When near the origin the right hand side grows not faster than third degree homogeneous function, we show that if a non-negative viscosity solution vanishes at a point, then it has to vanish everywhere.
