An optimal mass transport approach for limits of eigenvalue problems for the fractional pp-Laplacian

We find interpretation using optimal mass transport theory for eigenvalue problems obtained as limits of the eigenvalue problems for the fractional $p-$Laplacian operators as $p\to +\infty$. We deal both with Dirichlet and Neumann boundary conditions.Comment: 20 page

Space-weighted seismic attenuation mapping of the aseismic source of Campi Flegrei 1983-84 unrest

Peer reviewedPublisher PD

Interior penalty discontinuous Galerkin FEM for the p(x)p(x)-Laplacian

In this paper we construct an "Interior Penalty" Discontinuous Galerkin method to approximate the minimizer of a variational problem related to the $p(x)-$Laplacian. The function $p:\Omega\to [p_1,p_2]$ is log H\"{o}lder continuous and $1<p_1\leq p_2<\infty$. We prove that the minimizers of the discrete functional converge to the solution. We also make some numerical experiments in dimension one to compare this method with the Conforming Galerkin Method, in the case where $p_1$ is close to one. This example is motivated by its applications to image processing.Comment: 26 pages, 2 figure

The stress-field variation on the italian active volcanic areas: the shear wave splitting monitoring

In the tex

Application of the spac method to ambient noise recorded in the vesuvius area (italy)

Noise measurements were recorded using a dense short-period seismic array in Terzigno (Naples), a town that is located about 6 km from the Vesuvius crater. The aim of this study was to calculate a surface velocity model of the area under investigation through the application of the Spatial Autocorrelation (SPAC) method, with the hypotheses that ambient noise is stationary both in time and space, and that it is composed of surface dispersive waves. The correct knowledge of the surface structure is an important goal in site-effects studies. Correlation coefficients were calculated as functions of the azimuth on noise recorded at pairs of equally spaced stations in the frequency range of 1-8 Hz. Then, the spatial average correlation coefficients were compared to estimates over long-term recordings. The results appear to validate the hypothesis that ambient noise can be considered as a stochastic process. The correlation-frequency curves have been fitted to Bessel functions, from which the Rayleigh wave dispersion curve has been calculated. A velocity model has been derived from the dispersion curve using both trial and error and a standard inversion procedure. The results are consistent with those obtained from array measurements in the area in other studies (Scarpa et al., 2003)

The use of seismic arrays to study the seismo-volcanic source. The example of Mt Etna and Stromboli Volcano.

The properties of volcanic tremor wavefields at Mt Etna Volcano, Italy, are investigated using data from two dense, small aperture arrays of short-period seismometers deployed on the North and South flank of the volcano. Spectral analysis shows that most of the seismic energy is associated with several, narrow spectral peaks spanning the 1–5 Hz frequency band. Analysis of simultaneous recordings indicates that most of these peaks are common to different sites, thus suggesting a source effect as the origin of this energy. Frequency-slowness analyses show a complex wavefield, where body- and surface-waves alternatively dominate depending on the frequency band and the component of motion taken into account. Using a probabilistic approach, we invert slowness data measured at two dense arrays for retrieving source location and extent. The joint inversion of slowness data from the two arrays points to different source locations. This observation is interpreted in terms of ray bending associated with lateral heterogeneity and/or strong topographic effects on wave propagation. Once the propagation effects are taken into account, the most probable source location is a shallow region encompassing the summit craters and the eruptive fissures active at the time of the experiment. Data from two dense arrays of short-period seismometers are used to retrieve source locations of the explosion quakes at Stromboli volcano. Slowness vectors estimated at both arrays with the zero-lag cross-correlation technique constitute the experimental data set. A probabilistic approach based on a grid search spanning the volcano interior is used to calculate the probability of the source location. Results show a shallow source, located beneath the crater area, at depths not greater than 500 m below the surface

A family of diameter-based eigenvalue bounds for quantum graphs

We establish a sharp lower bound on the first non-trivial eigenvalue of the Laplacian on a metric graph equipped with natural (i.e., continuity and Kirchhoff) vertex conditions in terms of the diameter and the total length of the graph. This extends a result of, and resolves an open problem from, [J. B. Kennedy, P. Kurasov, G. Malenov\'a and D. Mugnolo, Ann. Henri Poincar\'e 17 (2016), 2439--2473, Section 7.2], and also complements an analogous lower bound for the corresponding eigenvalue of the combinatorial Laplacian on a discrete graph. We also give a family of corresponding lower bounds for the higher eigenvalues under the assumption that the total length of the graph is sufficiently large compared with its diameter. These inequalities are sharp in the case of trees.Comment: Substantial revision of v1. The main result, originally for the first eigenvalue, has been generalised to the higher ones. The title has been changed and the proofs substantially reorganised to reflect the new result, and a section containing concluding remarks has been adde

On the classification of OADP varieties

The main purpose of this paper is to show that OADP varieties stand at an important crossroad of various main streets in different disciplines like projective geometry, birational geometry and algebra. This is a good reason for studying and classifying them. Main specific results are: (a) the classification of all OADP surfaces (regardless to their smoothness); (b) the classification of a relevant class of normal OADP varieties of any dimension, which includes interesting examples like lagrangian grassmannians. Following [PR], the equivalence of the classification in (b) with the one of quadro-quadric Cremona transformations and of complex, unitary, cubic Jordan algebras are explained.Comment: 13 pages. Dedicated to Fabrizio Catanese on the occasion of his 60th birthday. To appear in a special issue of Science in China Series A: Mathematic

Twin digital short period seismic Array Experiment at Stromboli Volcano

Two small arrays composed by short period (1 Hz) digital seismic stations, with an aperture of approximately 400 meters, were set up at Stromboli volcano (one at semaforo Labronzo, the other at Ginostra- Timpone del Fuoco) with the purpose of the spatial location of the high frequency source of the explosion quakes. About 75 explosion-quakes were recorded at both arrays, and constitute the available data base. We have planned to apply the zero-lag cross-correlation technique to the whole data set in order to obtain back-azimuth and apparent slowness of the coherent seismic phases. A preliminary analysis for both arrays show that the predominant back-azimuth for the first phase is oriented in the direction of , but not strictly coincident to, the crater area. Moreover some back-scattered arrivals are quite evident in the seismogram.INGV - Osservatorio VesuvianoUnpublishedope