论文标题
非稳定的dirichlet和neumann数据的过度确定边界问题
Overdetermined boundary problems with nonconstant Dirichlet and Neumann data
论文作者
论文摘要
在本文中，我们考虑了$ \ mathbf {r}^n $的有限域上的一般二阶半椭圆方程的过度确定边界问题，其中一个人都规定了解决方案的dirichlet和neumann数据。我们对数据不一定恒定并且方程系数可以取决于位置的情况很感兴趣，因此过度确定的问题通常不接受径向解。我们的主要结果是，在少数技术假设下，始终存在过度确定的边界问题的非平凡解决方案。
In this paper we consider the overdetermined boundary problem for a general second order semilinear elliptic equation on bounded domains of $\mathbf{R}^n$, where one prescribes both the Dirichlet and Neumann data of the solution. We are interested in the case where the data are not necessarily constant and where the coefficients of the equation can depend on the position, so that the overdetermined problem does not generally admit a radial solution. Our main result is that, nevertheless, under minor technical hypotheses nontrivial solutions to the overdetermined boundary problem always exist.
