论文标题
完全非线性抛物线障碍问题的规律性理论
Regularity theory for fully nonlinear parabolic obstacle problems
论文作者
论文摘要
我们研究解决抛物线障碍物问题的自由边界，并通过完全非线性扩散。我们表明，自由边界分为常规部分和一个单一的部分：在常规点附近，自由边界在时空上为$ c^\ infty $。此外，我们证明，尺寸$ n-1 $的Lipschitz歧管本地涵盖了一组单数点，这也是$ \ varepsilon $ -flat在太空中，对于任何$ \ varepsilon> 0 $。
We study the free boundary of solutions to the parabolic obstacle problem with fully nonlinear diffusion. We show that the free boundary splits into a regular and a singular part: near regular points the free boundary is $C^\infty$ in space and time. Furthermore, we prove that the set of singular points is locally covered by a Lipschitz manifold of dimension $n-1$ which is also $\varepsilon$-flat in space, for any $\varepsilon>0$.
