论文标题
Hölder规律性的抛物线分数$ P $ -LAPLACIAN
Hölder regularity for parabolic fractional $p$-Laplacian
论文作者
论文摘要
为某些弱解决方案建立了本地Hölder的规律性，以用于一类抛物线分数$ p $ laplace方程，仅可测量可测量的内核。该证明使用Degiorgi的迭代，并完善了Dibenedetto的内在缩放方法。在振荡降低中，对溶液的非局部积分的控制起着至关重要的作用，并且需要在这种内在的缩放场景中进行精致的分析。以任何对数估计和任何比较原则分配，即使对于线性案例，该证明都是新的。
Local Hölder regularity is established for certain weak solutions to a class of parabolic fractional $p$-Laplace equations with merely measurable kernels. The proof uses DeGiorgi's iteration and refines DiBenedetto's intrinsic scaling method. The control of a nonlocal integral of solutions in the reduction of oscillation plays a crucial role and entails delicate analysis in this intrinsic scaling scenario. Dispensing with any logarithmic estimate and any comparison principle, the proof is new even for the linear case.
