论文标题
一维规定的曲率方程式通过强最大原理的最佳规律性结果
Optimal regularity results for the one-dimensional prescribed curvature equation via the strong maximum principle
论文作者
论文摘要
强大的最大原理的精致版本已被证明是一类二阶的普通微分方程，并可能是不连续的非单调性非线性。然后，利用该工具，洛佩兹·戈梅斯和奥马里最近建立的一些最佳规律性结果，用于通过一维曲率算子驱动的非自主式准线性方程的有界变化溶液，通过接纳一般规定的弯曲和结合一般边界条件，从而显着改善了一维曲率操作员。这里开发的新方法对我们以前的论文中提出的假设产生了一种新的，更深入的解释，同时阐明了它们的含义，并使他们完全透明地与强大的最大原则保持联系。
A refined version of the strong maximum principle is proven for a class of second order ordinary differential equations with possibly discontinuous non-monotone nonlinearities. Then, exploiting this tool, some optimal regularity results recently established by Lopez-Gomez and Omari, for the bounded variation solutions of non-autonomous quasilinear equations driven by the one-dimensional curvature operator, are substantially improved by admitting general prescribed curvatures and by incorporating general boundary conditions. The new approach developed here yields a new, deeper, interpretation of the assumptions introduced in our previous papers, simultaneously clarifying their meaning and making fully transparent their connection with the strong maximum principle.
