论文标题
关于障碍物问题的对数表皮不平等现象
On the logarithmic epiperimetric inequality for the obstacle problem
论文作者
论文摘要
我们给出了三种不同的证据，以解决障碍物问题的单数点处的对数 - 图表不平等。在第一个直接证明中，我们明确地写了竞争对手。第二个证据也是建设性的，但是这次竞争者是通过在球体上解决进化问题的解决方案给出的。我们比较了在不同的证据中获得的竞争对手，及其与最近出现的其他类似结果的关系。最后，在附录中，我们给出了一个一般定理，该定理也可以在其他情况下应用，在其他情况下，竞争对手的构建被简化为找到满足两个差异不平等的流程。
We give three different proofs of the log-epiperimetric inequality at singular points for the obstacle problem. In the first, direct proof, we write the competitor explicitly; the second proof is also constructive, but this time the competitor is given through the solution of an evolution problem on the sphere. We compare the competitors obtained in the different proofs and their relation to other similar results that appeared recently. Finally, in the appendix, we give a general theorem, which can be applied also in other contexts and in which the construction of the competitor is reduced to finding a flow satisfying two differential inequalities.
