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We consider degenerate Kolmogorov–Fokker–Planck operators L u = ∑ i , j = 1 m 0 a ij ( x , t ) ∂ x i x j 2 u + ∑ k , j = 1 N b jk x k ∂ x j u - ∂ t u ≡ ∑ i , j = 1 m 0 a ij ( x , t ) ∂ x i x j 2 u + Y u (with ( x , t ) ∈ R N + 1 and 1 ≤ m 0 ≤ N ) such that the corresponding model operator having constant a ij is hypoelliptic, translation invariant w.r.t. a Lie group operation in R N + 1 and 2-homogeneous w.r.t. a family of nonisotropic dilations. The matrix ( a ij ) i , j = 1 m 0 is symmetric and uniformly positive on R m 0 . The coefficients a ij are bounded and Dini continuous in space , and only bounded measurable in time. This means that, setting ( i ) S T = R N × - ∞ , T , ( ii ) ω f , S T ( r ) = sup ( x , t ) , ( y , t ) ∈ S T ‖ x - y ‖ ≤ r | f ( x , t ) - f ( y , t ) | ( iii ) ‖ f ‖ D ( S T ) = ∫ 0 1 ω f , S T ( r ) r d r + ‖ f ‖ L ∞ S T we require the finiteness of ‖ a ij ‖ D ( S T ) . We bound ω u x i x j , S T , ‖ u x i x j ‖ L ∞ ( S T ) ( i , j = 1 , 2 , . . . , m 0 ), ω Y u , S T , ‖ Y u ‖ L ∞ ( S T ) in terms of ω L u , S T , ‖ L u ‖ L ∞ ( S T ) and ‖ u ‖ L ∞ S T , getting a control on the uniform continuity in space of u x i x j , Y u if L u is bounded and Dini-continuous in space. Under the additional assumption that both the coefficients a ij and L u are log-Dini continuous, meaning the finiteness of the quantity ∫ 0 1 ω f , S T r r log r d r , we prove that u x i x j and Yu are Dini continuous; moreover, in this case, the derivatives u x i x j are locally uniformly continuous in space and time .

The KM3NeT collaboration started to build a multi-km3neutrino telescope in the Mediterranean Sea. The telescope is composed of two parts: the ARCA detector, optimised for searches for high energy neutrino sources in the Universe, and ORCA, for the determination of the mass hierarchy of neutrinos. ARCA is under construction at the Capo Passero site, Italy, 80 km offshore at a depth of 3500 m while ORCA is located in the Toulon area, France, 40 km offshore at a depth of 2500 m. The basic detection element of the KM3NeT detector is the Digital Optical Module. The module is a pressure resistant glass sphere, containing 31 photo-multiplier tubes. Eighteen modules are arranged in the detection unit, a vertical structure anchored on the sea floor. The detection units are deployed on the sea bed to form a three-dimensional array of optical modules to detect Cherenkov light produced by neutrino-induced muons. In these proceedings preliminary results obtained with the first two detection units of ARCA are presented. The capability to select and reconstruct atmospheric muons is discussed. The dependence of the muon flux with the sea depth is derived, showing that the detector is well calibrated and the systematics are kept under control.

Advanced  LIGO detected a significant gravitational wave signal (GW170104) originating from the coalescence of two black holes during the second observation run on January 4th, 2017. An all-sky high-energy neutrino follow-up search has been made using data from the Antares  neutrino telescope, including both upgoing and downgoing events in two separate analyses. No neutrino candidates were found within ± 500  s around the GW event time nor any time clustering of events over an extended time window of ± 3  months. The non-detection is used to constrain isotropic-equivalent high-energy neutrino emission from GW170104 to less than ∼ 1.2 × 10 55  erg for a E - 2 spectrum. This constraint is valid in the energy range corresponding to the 5–95% quantiles of the neutrino flux [3.2 TeV; 3.6 PeV], if the GW emitter was below the Antares horizon at the alert time.

The paper describes and reports the first results from a unique field experiment taking place at Lido Adriano (Italy). The project started in March 2003 having as main object the pressure maintenance of the gas reservoir to control coastline subsidence obtained by injection of sea water at about 4,000 m depth. Preliminary results analyzed during the early injection phase were encouraging. During this period 150 m³/day were pumped down (a total of 160,000 m³). The pressure monitoring during the period 2003-2006 showed an increase of pressure of 25 bars due to the injection activity. In the future the project will increase the injection rate to 2500 m³/day. An interesting \"environmentally sustainable\" aspect of the project is the use of sea-water for reinjection, using water filtered through Beach Drainage Systems that have the double role of enhancing beach stabilization.

The next generation of water Cherenkov neutrino telescopes in the Mediterranean Sea are under construction offshore France (KM3NeT/ORCA) and Sicily (KM3NeT/ARCA). The KM3NeT/ORCA detector features an energy detection threshold which allows to collect atmospheric neutrinos to study flavour oscillation. This paper reports the KM3NeT/ORCA sensitivity to this phenomenon. The event reconstruction, selection and classification are described. The sensitivity to determine the neutrino mass ordering was evaluated and found to be 4.4σ if the true ordering is normal and 2.3σ if inverted, after 3 years of data taking. The precision to measure Δm322 and θ23 were also estimated and found to be 85.10-6eV2 and (-3.1+1.9)∘ for normal neutrino mass ordering and, 75.10-6eV2 and (-7.0+2.0)∘ for inverted ordering. Finally, a unitarity test of the leptonic mixing matrix by measuring the rate of tau neutrinos is described. Three years of data taking were found to be sufficient to exclude event rate variations larger than 20% at 3σ level.

In March 2013, the Nemo Phase-2 tower was successfully deployed at 80 km off-shore Capo Passero (Italy) at 3500 m depth. The tower operated continuously until August 2014. We present the results of the atmospheric muon analysis from the data collected in 411 days of live time. The zenith-angle distribution of atmospheric muons was measured and results compared with Monte Carlo simulations. The associated depth intensity relation was then measured and compared with previous measurements and theoretical predictions.

KM3NeT is a research infrastructure located in the Mediterranean Sea, that will consist of two deep-sea Cherenkov neutrino detectors. With one detector (ARCA), the KM3NeT Collaboration aims at identifying and studying TeV–PeV astrophysical neutrino sources. With the other detector (ORCA), the neutrino mass ordering will be determined by studying GeV-scale atmospheric neutrino oscillations. The first KM3NeT detection units were deployed at the Italian and French sites between 2015 and 2017. In this paper, a description of the detector is presented, together with a summary of the procedures used to calibrate the detector in-situ. Finally, the measurement of the atmospheric muon flux between 2232–3386 m seawater depth is obtained.

The KM3NeT research infrastructure is unconstruction in the Mediterranean Sea. KM3NeT will study atmospheric and astrophysical neutrinos with two multi-purpose neutrino detectors, ARCA and ORCA, primarily aimed at GeV–PeV neutrinos. Thanks to the multi-photomultiplier tube design of the digital optical modules, KM3NeT is capable of detecting the neutrino burst from a Galactic or near-Galactic core-collapse supernova. This potential is already exploitable with the first detection units deployed in the sea. This paper describes the real-time implementation of the supernova neutrino search, operating on the two KM3NeT detectors since the first months of 2019. A quasi-online astronomy analysis is introduced to study the time profile of the detected neutrinos for especially significant events. The mechanism of generation and distribution of alerts, as well as the integration into the SNEWS and SNEWS 2.0 global alert systems, are described. The approach for the follow-up of external alerts with a search for a neutrino excess in the archival data is defined. Finally, an overview of the current detector capabilities and a report after the first two years of operation are given.

A bstract KM3NeT/ORCA is a next-generation neutrino telescope optimised for atmospheric neutrino oscillations studies. In this paper, the sensitivity of ORCA to the presence of a light sterile neutrino in a 3+1 model is presented. After three years of data taking, ORCA will be able to probe the active-sterile mixing angles θ 14 , θ 24 , θ 34 and the effective angle θ μe , over a broad range of mass squared difference ∆ m 41 2 ∼ [10 − 5 , 10] eV 2 , allowing to test the eV-mass sterile neutrino hypothesis as the origin of short baseline anomalies, as well as probing the hypothesis of a very light sterile neutrino, not yet constrained by cosmology. ORCA will be able to explore a relevant fraction of the parameter space not yet reached by present measurements.