We consider a class of semilinear elliptic problems in twoand three-dimensional domains with conical points. We introduce Sobolev spaces with detached asymptotics generated by the asymptotical behaviour of solutions of corresponding linearized problems near conical boundary points. We show that the corresponding nonlinear operator acting between these spaces is Fréchet differentiable. Applying ...

This paper continues the authors’ previous study (SIAM J. Math. Anal., 2016) of the trend toward equilibrium of the Becker-Döring equations with subcritical mass, by characterizing certain fine properties of solutions to the linearized equation. In particular, we partially characterize the spectrum of the linearized operator, showing that it contains the entire imaginary axis in polynomially we...

We investigate the spectrum of the linear operator coming from the sine-Gordon equation linearized about a travelling kink-wave solution. Using various geometric techniques as well as some elementary methods from ODE theory, we find that the point spectrum of such an operator is purely imaginary provided the wave speed c of the travelling wave is not ±1. We then compute the essential spectrum o...

The theory of linearized general relativity is quantized using the projection operator formalism, in which no gauge choices are made. The result of this exercise is the construction of a separable, reproducing kernel for the physical Hilbert space using coherent states. The work is then compared with legacy canonical quantum gravity results.

Linearized asymptotic inversion of seismic data maps, given the smooth variations in medium properties such as phase velocities (the background medium), known information on the wavefront set of the data into the unknown singular component of medium variations (the medium contrast). Such inversion was formulated in terms of a Maslov extension of Generalized Radon Transforms, and allows the form...

We present recent results [4, 28, 29] about the quantitative study of the linearized Boltzmann collision operator, and its application to the study of the trend to equilibrium for the spatially homogeneous Boltzmann equation for hard spheres.

We study the spectral structure of the complex linearized operator for a class of nonlinear Schrödinger systems, obtaining as byproduct some interesting properties of non-degenerate ground state of the associated elliptic system, such as being isolated and orbitally stable.

There is an embedding of affine vertex algebras $V^k(\mathfrak{gl}_n) \hookrightarrow V^k(\mathfrak{sl}_{n+1})$, and the coset $\mathcal{C}^k(n) = \text{Com}(V^k(\mathfrak{gl}_n), V^k(\mathfrak{sl}_{n+1}))$ a natural generalization parafermion algebra $\mathfrak{sl}_2$. It was called generalized parafermions by third author shown to arise as one-parameter quotient universal two-parameter $\math...

We have been working on a long term program to construct the first time-periodic solutions of the compressible Euler equations. Our program from the start has been to construct the simplest periodic wave structure, and then tailor the analysis in a rigorous existence proof to the explicit structure. In [26] have found the periodic structure, in [27, 28] we showed that linearized solutions with ...