论文标题
非线性抛物线运营商的全球梯度估计
Global gradient estimates for nonlinear parabolic operators
论文作者
论文摘要
我们考虑由非线性扩散操作员驱动的抛物线方程，并在方程式发生的域中获得梯度估计。 该估计值取决于方程的结构常数，环境空间的几何形状以及初始和边界数据。 作为副产品，人们很容易获得通用的室内估计，而不是取决于抛物线数据。 考虑的设置包括采购条款和一般扩散系数。据我们所知，即使在欧几里得的环境中，结果也是新的，尽管我们在这里也对待完整的Riemannian歧管也是如此。
We consider a parabolic equation driven by a nonlinear diffusive operator and we obtain a gradient estimate in the domain where the equation takes place. This estimate depends on the structural constants of the equation, on the geometry of the ambient space and on the initial and boundary data. As a byproduct, one easily obtains a universal interior estimate, not depending on the parabolic data. The setting taken into account includes sourcing terms and general diffusion coefficients. The results are new, to the best of our knowledge, even in the Euclidean setting, though we treat here also the case of a complete Riemannian manifold.
