Title: Uniqueness and nondegeneracy of least-energy solutions to fractional Dirichlet problems Show Chinese title

Title: 最小能量解的唯一性和非退化性到分数狄利克雷问题

Abstract: We prove the uniqueness and nondegeneracy of least-energy solutions of a fractional Dirichlet semilinear problem in sufficiently large balls and in more general symmetric domains. Our proofs rely on uniform estimates on growing domains, on the uniqueness and nondegeneracy of the ground state of the problem in RN , and on a new symmetry characterization of the eigenfunctions of the linearized eigenvalue problem in domains which are convex in the x1 - direction and symmetric with respect to a hyperplane reflection. Show Chinese abstract

Abstract: 我们证明了在足够大的球体和更一般的对称域中，分数Dirichlet非线性问题的最小能量解的唯一性和非退化性。 我们的证明依赖于在扩展域上的统一估计，RN中该问题基态的唯一性和非退化性，以及在关于超平面反射对称且在x1方向上凸的域中，线性化特征值问题特征函数的新对称性特征。