论文标题
与梯度退化的分数椭圆方程的内部规律性结果
Interior regularity results for fractional elliptic equations that degenerate with the gradient
论文作者
论文摘要
在本文中，我们获得了溶液梯度消失的非本地dirichlet问题的粘度解决方案的内部规律性估计。当分数扩散的顺序小于或等于一个时，获得内部Hölder估计值，而Lipschitz估计它大于一个。在后一种情况下，估计值足够强大，可以通过改进平坦性程序来结论内部$ c^{1，α} $规律性，当非局部项足够接近二阶扩散时，这是可能的。
In this paper we obtain interior regularity estimates for viscosity solutions of nonlocal Dirichlet problems that degenerate when the gradient of the solution vanishes. Interior Hölder estimates are obtained when the order of the fractional diffusion is less or equal than one, and Lipschitz estimates when it is bigger than one. In the latter case, the estimates are robust enough to conclude interior $C^{1, α}$ regularity by an improvement of the flatness procedure, which is possible when the nonlocal term is close enough to a second-order diffusion.
