## 1,249 Citations

Propagation of polarization in transmission problems

- MathematicsPure 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

- MathematicsMATHEMATICA SCANDINAVICA
- 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

- Mathematics
- 2020

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

- MathematicsInventiones mathematicae
- 2018

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

- Mathematics
- 2016

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

- Mathematics
- 2011

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

- Mathematics
- 2010

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

- Mathematics
- 2009

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

- Mathematics
- 2009

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

- Mathematics
- 2009

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…