双障碍问题与具有非严格凸梯度约束的全非线性 PDE
偏微分方程分析
2021-01-28 v2
摘要
我们证明了带凸梯度约束的全非线性椭圆方程的最优 W^{2,∞} 正则性。我们不假设约束的任何正则性；因此约束不必为 C^1 或严格凸。我们还证明了该最优正则性可保持到边界。我们的方法是表明这些带梯度约束的椭圆方程与某些全非线性双障碍问题相关。随后我们证明了双障碍问题的最优 W^{2,∞} 正则性。在此过程中，我们还运用了障碍物二阶导数的单调性，此性质已在先前工作中获得。
引用
@article{arxiv.1907.04683,
title = {Double obstacle problems and fully nonlinear PDE with non-strictly convex gradient constraints},
author = {Mohammad Safdari},
journal= {arXiv preprint arXiv:1907.04683},
year = {2021}
}
备注
The previous title of this article was "Fully nonlinear elliptic equations with non-strictly convex gradient constraints, and fully nonlinear double obstacle problems". 35 pages. arXiv admin note: substantial text overlap with arXiv:1807.01590