8 citations · 41 across the 11 of their papers we have counts for
11 papers
On the asymptotic behaviour of the restricted Dirichlet Laplacian of real order on stretching tubes
Roberta Musina, Giulio Romani
We study spectral and variational properties of the (possibly) fractional Dirichlet Laplacian , , on bounded subsets of $\mathbb R^n\times\mathbb R^…
Nonlocal planar Schrödinger-Poisson systems in the fractional Sobolev limiting case
Daniele Cassani, Zhisu Liu, Giulio Romani
We study the nonlinear Schrödinger equation for the fractional Laplacian strongly coupled with the Poisson equation in dimension two and with , which is the limi…
Symmetry and uniqueness for a hinged plate problem in a ball
Giulio Romani
In this paper we address some questions about symmetry, radial monotonicity, and uniqueness for a semilinear fourth-order boundary value problem in the ball of derivi…
Perturbed eigenvalues of polyharmonic operators in domains with small holes
Veronica Felli, Giulio Romani
We study singular perturbations of eigenvalues of the polyharmonic operator on bounded domains under removal of small interior compact sets. We consider both homogeneous Dirichlet…
A quasilinear transmission problem with application to Maxwell equations with a divergence-free -field
Tomáš Dohnal, Giulio Romani, Daniel P. Tietz
Maxwell equations in the absence of free charges require initial data with a divergence free displacement field . In materials in which the dependence $\mathcal D=\math…
Justification of the Asymptotic Coupled Mode Approximation of Out-of-Plane Gap Solitons in Maxwell Equations
Tomáš Dohnal, Giulio Romani
In periodic media gap solitons with frequencies inside a spectral gap but close to a spectral band can be formally approximated by a slowly varying envelope ansatz. The ansatz is b…
Eigenvalue Bifurcation in Doubly Nonlinear Problems with an Application to Surface Plasmon Polaritons
Tomáš Dohnal, Giulio Romani
We consider a class of generally non-self-adjoint eigenvalue problems which are nonlinear in the solution as well as in the eigenvalue parameter ("doubly" nonlinear). We prove a bi…
Differences between fundamental solutions of general higher order elliptic operators and of products of second order operators
Hans-Christoph Grunau, Giulio Romani, Guido Sweers
We study fundamental solutions of elliptic operators of order with constant coefficients in large dimensions , where their singularities become unbounded. For co…
A-priori bounds for a quasilinear problem in critical dimension
Giulio Romani
We establish uniform a-priori bounds for solutions of the quasilinear problem in , with on , where is a bounded smooth and c…
Uniform bounds for higher-order semilinear problems in conformal dimension
Gabriele Mancini, Giulio Romani
We establish uniform a-priori estimates for solutions of the semilinear Dirichlet problem \begin{equation} \begin{cases} (-Δ)^m u=h(x,u)\quad&\mbox{in }Ω,\\ u=\partial_nu=\cdots=\p…
Positivity for fourth-order semilinear problems related to the Kirchhoff-Love functional
Giulio Romani
We study the ground states of the following generalization of the Kirchhoff-Love functional, where …