The Analysis of Linear Partial Differential Operators III

  title={The Analysis of Linear Partial Differential Operators III},
  author={Lars H{\"o}rmander},
Propagation of polarization in transmission problems
  • S. Hansen
  • Mathematics
    Pure and Applied Analysis
  • 2022
For geometric systems of real principal type, we define a subprincipal symbol and derive a transport equation for polarizations which, in the scalar case, is a well-known equation of Duistermaat and
Exact Green's formula for the fractional Laplacian and perturbations
  • G. Grubb
  • Mathematics
  • 2020
Let Ω be an open, smooth, bounded subset of $ \mathbb{R}^n $. In connection with the fractional Laplacian $(-\Delta )^a$ ($a>0$), and more generally for a $2a$-order classical pseudodifferential
The Weyl problem in warped product spaces
In this paper, we discuss the Weyl problem in warped product spaces. We apply the method of continuity and prove the openness of the Weyl problem. A counterexample is constructed to show that the
Time quasi-periodic gravity water waves in finite depth
We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions—namely periodic and even in the space variable x—of a
Forward and backward in time Cauchy problems for systems of parabolic‐type PDE with a small parameter
The paper introduces a class of functions where the resolving operator for a system of Kolmogorov–Feller‐type equations with a small parameter is well posed in forward and backward times. The
Local energy decay for the wave equation with a time-periodic non-trapping metric and moving obstacle
Consider the mixed problem with Dirichelet condition associated to the wave equation ∂ 2 u - divx(a(t,x)∇xu) = 0, where the scalar metric a(t,x) is T-periodic in t and uniformly equal to 1 outside a
Singular support of the scattering kernel for the rayleigh wave in perturbed half-spaces
Abstract. This paper deals with the Rayleigh wave scattering on perturbed half-spaces in the framework of the Lax-Phillips type. Singular parts of the scattering kernel for this scattering are
Gradient estimates for the eigenfunctions on compact manifolds with boundary and Hörmander Multiplier Theorem
Abstract On compact Riemannian manifolds (M,g) of dimension n ≥ 2 with smooth boundary, the gradient estimates for the eigenfunctions of the Dirichlet Laplacian are proved by the maximum principle.
Invariants of Isospectral Deformations and Spectral Rigidity
We introduce a notion of weak isospectrality for continuous deformations. Consider the Laplace–Beltrami operator on a compact Riemannian manifold with Robin boundary conditions. Given a Kronecker
The Petrovskii correctness and semigroups of operators
Let $P(\partial/\partial x)$ be an $m\times n$ matrix whose entries are PDO on $\bbR^n$ with constant coefficients, and let $\calS(\bbR^n)$ be the space of infinitely differentiable rapidly