R. Bramati

activity

20192026

collaborators

Showing math.APShow all

4 papers · 1 filter

math.AP2026

Grushin spherical harmonics in non-degenerate dimension one

Roberto Bramati, Paolo Luzzini

The Grushin Laplacian $Δ_{α} = Δ_{x} + ∣ x ∣^{2 α} Δ_{y}$ is a degenerate elliptic operator in $R^{h + k}$ that degenerates on ${0} \times R^{k}$ . We explicitly compute the Gr…

math.AP2024

Periodic layer potentials and domain perturbations

Roberto Bramati, Matteo Dalla Riva, Paolo Luzzini +1

In this paper, we review the construction of periodic fundamental solutions and periodic layer potentials for various differential operators. Specifically, we focus on the Laplace…

math.AP2022

The Functional Analytic Approach for quasi-periodic boundary value problems for the Helmholtz equation

Roberto Bramati, Matteo Dalla Riva, Paolo Luzzini +1

We lay down the preliminary work to apply the Functional Analytic Approach to quasi-periodic boundary value problems for the Helmholtz equation. This consists in introducing a quas…

math.AP2022

Continuous harmonic functions on a ball that are not in $H^{s}$ for $s > 1/2$

Roberto Bramati, Matteo Dalla Riva, Brian Luczak

We show that there are harmonic functions on a ball $B_{n}$ of $R^{n}$ , $n \geq 2$ , that are continuous up to the boundary (and even Hölder continuous) but not in the…

Grushin spherical harmonics in non-degenerate dimension one

Periodic layer potentials and domain perturbations

The Functional Analytic Approach for quasi-periodic boundary value problems for the Helmholtz equation

Continuous harmonic functions on a ball that are not in Hs for s>1/2

Continuous harmonic functions on a ball that are not in $H^{s}$ for $s > 1/2$