A symmetry result for cooperative elliptic systems with singularities

We obtain symmetry results for solutions of an elliptic system of equation possessing a cooperative structure. The domain in which the problem is set may possess "holes" or "small vacancies" (measured in terms of capacity) along which the solution may diverge. The method of proof relies on the moving plane technique, which needs to be suitably adapted here to take care of the complications arising from the vacancies in the domain and the analytic structure of the elliptic system

A symmetry result for cooperative elliptic systems with singularities

We obtain symmetry results for solutions of an elliptic system of equationpossessing a cooperative structure. The domain in which the problem is set maypossess "holes" or "small vacancies" (measured in terms of capacity) along which thesolution may diverge.The method of proof relies on the moving plane technique, which needs to besuitably adapted here to take care of the complications arising from the vacancies inthe domain and the analytic structure of the elliptic system

Definition of the Local Geoid Undulation Using Non-contemporary GNSS-Levelling Data on Subsidence Area: Application on the Adriatic Coastline

The knowledge of the so-called geoid undulation, which represents the height of the geoid above a reference ellipsoid, is a fundamental step to link ellipsoidal heights measured using satellite systems and orthometric heights. Several geoid models are available at the time both at the national or global scale, which can be used for the purpose. Another way to define the geoid undulation is to perform joint measures with GNSS and spirit levelling over common benchmarks. This requires onerous measurements that is seldom possible to perform due to their cost. In this work, we evaluated the possibility to define a local model of the geoid undulation using already available spirit levelling orthometric heights and GNSS ellipsoidal heights measured about 13 years later. The test area is the Emilia-Romagna Adriatic coastline, an area of great interest both from the environmental and economic point of view, which is also undergoing consistent subsidence phenomena. Test results show that the available measurements allow defining a geoid undulation that is coherent with the shape defined by the gravimetric models and also allows to transform ellipsoidal heights into orthometric ones more consistent with the height reference available on the surveyed area. A 7 cm overall bias with respect to the ITALGEO05 was found, whereas ITG2009 and EGM2008 have higher differences. The use of subsidence models to align over time the coordinates used to define the geoid undulation has proven to be a fundamental step. The analysis on the a-priori uncertainty in the geoid height definition shown that the combined use of much more precise GNSS coordinates and contemporary spirit levelling campaign is necessary to significantly improve the resulting geoid height

Spectral Filtering of the Spatial Green\u2019s Function

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Semilinear elliptic equations involving mixed local and nonlocal operators

In this paper, we consider an elliptic operator obtained as the superposition of a classical second-order differential operator and a nonlocal operator of fractional type. Though the methods that we develop are quite general, for concreteness we focus on the case in which the operator takes the form $-\Delta+(-\Delta)^s$, with $s\in(0,1)$. We focus here on symmetry properties of the solutions and we prove a radial symmetry result, based on the moving plane method, and a one-dimensional symmetry result, related to a classical conjecture by G.W. Gibbons

Government policies to enhance access to credit for infrastructure-based PPPs:an approach to classification and appraisal

Analysis of ways the public sector can ease the use of private money for infrastructure financing

Thin glass shells for active optics for future space telescopes

We present a method for the manufacturing of thin shells of glass, which appears promising for the development of active optics for future space telescopes. The method exploits the synergy of different mature technologies, while leveraging the commercial availability of large, high-quality sheets of glass, with thickness up to few millimeters. The first step of the method foresees the pre-shaping of flat substrates of glass by replicating the accurate shape of a mold via hot slumping technology. The replication concept is advantageous for making large optics composed of many identical or similar segments. After the hot slumping, the shape error residual on the optical surface is addressed by applying a deterministic sub-aperture technology as computer-controlled bonnet polishing and/or ion beam figuring. Here we focus on the bonnet polishing case, during which the thin, deformable substrate of glass is temporary stiffened by a removable holder. In this paper, we report on the results so far achieved on a 130 mm glass shell case study.Comment: This is a pre-print of an article published in CEAS Space Journal. The final authenticated version is available online at: http://link.springer.com/article/10.1007/s12567-019-00259-