论文标题
Hadamard公式和非本地特征问题问题
The Hadamard formula and the Rayleigh-Faber-Krahn inequality for nonlocal eigenvalue problems
论文作者
论文摘要
在本文中，我们获得了简单特征值的Hadamard类型公式，以及类似于一类非局部特征值问题的Rayleigh-Faber-Krahn不等式。这样的方程式包括Dirichlet和Neumann条件的经典非本地问题。 Hadamard公式是计算出来的，允许通过$ n $二维的Riemannian歧管（可能具有有限量的边界）的嵌入域扰动，而重排技术则显示了Rayleigh-Faber-Krahn不平等。
In this paper we obtain a Hadamard type formula for simple eigenvalues and an analog to the Rayleigh-Faber-Krahn inequality for a class of nonlocal eigenvalue problems. Such class of equations include among others, the classical nonlocal problems with Dirichlet and Neumann conditions. The Hadamard formula is computed allowing domain perturbations given by embeddings of $n$-dimensional Riemannian manifolds (possibly with boundary) of finite volume while the Rayleigh-Faber-Krahn inequality is shown by rearrangement techniques.
