论文标题
与Finsler Laplacian相关的过度确定问题
An overdetermined problem associated to the Finsler Laplacian
论文作者
论文摘要
我们证明了各向异性拉普拉斯的刚性结果。更确切地说，问题的结构域是由一个未知的表面界定的，该表面支持Dirichlet条件，并与Neumann-type条件一起进行，这不是翻译不变的。使用比较参数，我们表明该域实际上是沃尔夫的形状。我们还考虑了更普遍的情况，当需要未知表面在给定的圆锥形表面上具有边界：在这种情况下，问题的域被未知的表面和一部分给定圆锥形表面的一部分界定，这支持了均匀的neumann条件。我们证明未知的表面位于沃尔夫形状的边界上。
We prove a rigidity result for the anisotropic Laplacian. More precisely, the domain of the problem is bounded by an unknown surface supporting a Dirichlet condition together with a Neumann-type condition which is not translation-invariant. Using a comparison argument, we show that the domain is in fact a Wulff shape. We also consider the more general case when the unknown surface is required to have its boundary on a given conical surface: in such a case, the domain of the problem is bounded by the unknown surface and by a portion of the given conical surface, which supports a homogeneous Neumann condition. We prove that the unknown surface lies on the boundary of a Wulff shape.
