论文标题
Keldysh操作员的分析性低下
Analytic hypoellipticity of Keldysh operators
论文作者
论文摘要
我们考虑Keldysh型操作员，$ p = x_1 d_ {x_1}^2 + a（x）d_ {x_1} + q（x，x，d_ {x'}）$，$ x =（x_1，x'）$带有分析系数，以及$ q（x，x，x，x，x，d_ {x'} $ n off in n off in n office，对于$ x $接近零。我们表明，如果$ p u = f $，$ u \ in c^\ infty $，而$ f $在$ 0 $ 0 $的社区中进行分析，那么$ u $在$ 0 $的社区中进行分析。这是对带有拉格朗日径向集合的任何顺序的运算符的微局部结果有效的结果。我们的结果证明了第二作者和勒博做出的猜想的广义版本，并在散射理论中有应用。
We consider Keldysh-type operators, $ P = x_1 D_{x_1}^2 + a (x) D_{x_1} + Q (x, D_{x'} ) $, $ x = ( x_1, x') $ with analytic coefficients, and with $ Q ( x, D_{x'} ) $ second order, principally real and elliptic in $ D_{x'} $ for $ x $ near zero. We show that if $ P u =f $, $ u \in C^\infty $, and $ f $ is analytic in a neighbourhood of $ 0 $ then $ u $ is analytic in a neighbourhood of $ 0 $. This is a consequence of a microlocal result valid for operators of any order with Lagrangian radial sets. Our result proves a generalized version of a conjecture made by the second author and Lebeau and has applications to scattering theory.
