标题： Hölder正则性对于非变分型多孔介质类型方程 显示英文标题

标题： Hölder regularity for non-variational porous media type equations

摘要： 我们提出了一种Krylov-Safonov理论方法，用于非变分型多孔介质方程的粘性解的Hölder正则性。 我们探讨了此类问题的独特性：或者方程处于一致椭圆 regime，或者射线机制负责正则性。 我们的技术基于滑动抛物面，从而得到一种ABP类型的测度估计。 通过结合这些估计，可以获得振荡减小的性质，从而在Hölder空间中实现正则性控制。 显示英文摘要

摘要： We present a Krylov-Safonov theory approach for the H\"older regularity of viscosity solutions to non-variational porous media type equations. We explore the peculiarity of this type of problem: either the equation falls in a uniformly elliptic regime or the eikonal mechanism takes care of the regularity. Our techniques are based on sliding paraboloids resulting in an ABP-type measure estimate. By combining such estimates, a diminishing of oscillation property is available, resulting in a regularity control in H\"older spaces.