论文标题
关于椭圆自由边界问题的非最小化解决方案
On nonminimizing solutions of elliptic free boundary problems
论文作者
论文摘要
我们提出了一个差异框架，用于研究不一定会最大程度减少能量的椭圆自由边界问题解决方案的存在和规律性。作为应用程序，我们获得了关键和亚临界超线性边界问题的Mountain Pass解决方案，并在尺寸$ n = 2 $中建立自由边界的完整规律性，并在更高维度中进行部分规律性。
We present a variational framework for studying the existence and regularity of solutions to elliptic free boundary problems that do not necessarily minimize energy. As applications, we obtain mountain pass solutions of critical and subcritical superlinear free boundary problems, and establish full regularity of the free boundary in dimension $N = 2$ and partial regularity in higher dimensions.
