论文标题
较高的Hölder规律性，用于混合局部和非局部退化椭圆方程
Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations
论文作者
论文摘要
我们考虑涉及本地和非本地退化$ p $ laplace运营商组合的方程式。该论文的主要贡献几乎是Lipschitz的规律性对于均匀方程，而Hölder的连续性在一般情况下具有明确的Hölder指数。对于某些参数，我们的结果也意味着梯度的Hölder连续性。此外，我们建立了存在，独特性和局部界限。该方法基于Moser精神的迭代与近似方法相结合。
We consider equations involving a combination of local and nonlocal degenerate $p$-Laplace operators. The main contribution of the paper is almost Lipschitz regularity for the homogeneous equation and Hölder continuity with an explicit Hölder exponent in the general case. For certain parameters, our results also imply Hölder continuity of the gradient. In addition, we establish existence, uniqueness and local boundedness. The approach is based on an iteration in the spirit of Moser combined with an approximation method.
