Hypoellipticity on time-periodic space-times
Sandro Coriasco, Perry Kleinhenz, Jared Wunsch
Abstract
We study the hypoellipticity of operators on a product type Lorentzian manifold where the time variable is periodic. In particular, we prove that hypoellipticity holds for such time-periodic equations, with a stronger estimate when the mass parameter or time period lies outside a set of arbitrarily small measure. We consider both compact and noncompact spatial manifolds and provide explicit examples involving the wave operator. The proof relies on a Fourier series decomposition and asymptotics for eigenvalue counting functions.
Create a lesson
Related papers
On the cut locus of Hamilton--Jacobi equations I: structure and propagation via the touching approach
Piermarco Cannarsa, Wei Cheng, Jiahui Hong \and Wenxue Wei
Global Well-posedness and Asymptotic Analysis of a Damped Nonlinear Wave Equation with a Codimension-One Constraint
Harsh Tiwari, Manil T. Mohan
Global smooth behavior in Kuznetsov and Westervelt type viscous wave equations: A unifying approach covering W1,q-small initial data
Tahir Boudjeriou, Michael Winkler
Maximizing the fundamental Laplace--Neumann eigenvalue on quadrilaterals
Ryoki Endo, Braxton Osting
Sharp convergence rates for the vanishing discount problem with hyperbolic Aubry sets
Panrui Ni
Divergence-Free Approximation in Sobolev and Lebesgue Spaces on General Unbounded Domains with Applications to Energy Equality in Fluid Dynamics
Akram Khan, Sagar Gautam, Manil T. Mohan