论文标题
Monge-ampère方程的内部估计值
Interior Estimates for Monge-Ampère Equation in Terms of Modulus of Continuity
论文作者
论文摘要
我们研究了蒙格 - 安培方程，但右边界值受到零边界值的影响，并以正右侧的统一为准是连续的或本质上是界限的。根据连续性模量，获得了解决方案第一和第二个衍生物的内部估计。我们阐明了估计值如何取决于各种数量，但使它们独立于解决方案的凸模模量。我们的主要定理有许多有用的后果。其中之一是溶液的HöldersIminors和右侧函数之间的非线性依赖性，这证实了Figalli，Jhaveri和Mooney的结果（J.Func。Anal。2016）。我们的技术部分受Jian和Wang（Siam J.Math。Anal。2007）的启发，其中包括使用一系列所谓的部分。
We investigate the Monge-Ampère equation subject to zero boundary value and with a positive right-hand side unction assumed to be continuous or essentially bounded. Interior estimates of the solution's first and second derivatives are obtained in terms of moduli of continuity. We explicate how the estimates depend on various quantities but have them independent of the solution's modulus of convexity. Our main theorem has many useful consequences. One of them is the nonlinear dependence between the Hölder seminorms of the solution and of the right-side function, which confirms the results of Figalli, Jhaveri and Mooney (J. Func. Anal. 2016). Our technique is in part inspired by Jian and Wang (SIAM J. Math. Anal. 2007) which includes using a sequence of so-called sections.
