论文标题
具有非均匀变性和应用的完全非线性模型的几何梯度估计值
Geometric Gradient Estimates For Fully Nonlinear Models With Non-Homogeneous Degeneracy and Applications
论文作者
论文摘要
我们为具有非均匀变性的一类完全非线性椭圆方程的有界溶液建立了尖锐的几何持有器规律性估计。这样的规律性估计通过完全不同的作案操作简化和推广。我们的方法基于几何切向方法，并利用了精制的振荡机制，结合了紧凑和缩放技术。最后，我们与各种非线性几何自由边界问题和椭圆PDE理论中的相关非线性问题提出了一些联系，这可能具有自身的兴趣。我们还提供了明确的例子，其中我们的结果很敏锐。
We establish sharp geometric Holder regularity estimates for Gradient for bounded solutions of a class of fully nonlinear elliptic equations with non-homogeneous degeneracy. Such regularity estimates simplify and generalize, to some extent, earlier ones via a totally different modus operandi. Our approach is based on geometric tangential methods and makes use of a refined oscillation mechanism combined with compactness and scaling techniques. In the end, we present some connections of our findings with a variety of nonlinear geometric free boundary problems and relevant nonlinear problems in the theory of elliptic PDEs, which may have their own interest. We also deliver explicit examples where our results are sharp.
