Commutator Criteria for Magnetic Pseudodifferential Operators

The gauge covariant magnetic Weyl calculus has been introduced and studied in previous works. We prove criteria in terms of commutators for operators to be magnetic pseudo-differential operators of suitable symbol classes. The approach is completely intrinsic; neither the statements nor the proofs depend on a choice of a vector potential. We apply this criteria to inversion problems, functional calculus, affiliation results and to the study of the evolution group generated by a magnetic pseudo-differential operator.Comment: Acknowledgements adde

Derivation of the Zakharov equations

This paper continues the study of the validity of the Zakharov model describing Langmuir turbulence. We give an existence theorem for a class of singular quasilinear equations. This theorem is valid for well-prepared initial data. We apply this result to the Euler-Maxwell equations describing laser-plasma interactions, to obtain, in a high-frequency limit, an asymptotic estimate that describes solutions of the Euler-Maxwell equations in terms of WKB approximate solutions which leading terms are solutions of the Zakharov equations. Because of transparency properties of the Euler-Maxwell equations, this study is led in a supercritical (highly nonlinear) regime. In such a regime, resonances between plasma waves, electromagnetric waves and acoustic waves could create instabilities in small time. The key of this work is the control of these resonances. The proof involves the techniques of geometric optics of Joly, M\'etivier and Rauch, recent results of Lannes on norms of pseudodifferential operators, and a semiclassical, paradifferential calculus

An optimal gap theorem

By solving the Cauchy problem for the Hodge-Laplace heat equation for $d$-closed, positive $(1, 1)$-forms, we prove an optimal gap theorem for K\"ahler manifolds with nonnegative bisectional curvature which asserts that the manifold is flat if the average of the scalar curvature over balls of radius $r$ centered at any fixed point $o$ is a function of $o(r^{-2})$. Furthermore via a relative monotonicity estimate we obtain a stronger statement, namely a `positive mass' type result, asserting that if $(M, g)$ is not flat, then $\liminf_{r\to \infty} \frac{r^2}{V_o(r)}\int_{B_o(r)}\mathcal{S}(y)\, d\mu(y)>0$ for any $o\in M$

The role of fundamental solution in Potential and Regularity Theory for subelliptic PDE

In this survey we consider a general Hormander type operator, represented as a sum of squares of vector fields plus a drift and we outline the central role of the fundamental solution in developing Potential and Regularity Theory for solutions of related PDEs. After recalling the Gaussian behavior at infinity of the kernel, we show some mean value formulas on the level sets of the fundamental solution, which are the starting point to obtain a comprehensive parallel of the classical Potential Theory. Then we show that a precise knowledge of the fundamental solution leads to global regularity results, namely estimates at the boundary or on the whole space. Finally in the problem of regularity of non linear differential equations we need an ad hoc modification of the parametrix method, based on the properties of the fundamental solution of an approximating problem

Observation of a sudden cessation of a very-high-energy gamma-ray flare in PKS 1510-089 with H.E.S.S. and MAGIC in May 2016

The flat spectrum radio quasar (FSRQ) PKS 1510-089 is known for its complex multiwavelength behavior, and is one of only a few FSRQs detected at very high energy (VHE, E >100 GeV) -rays. VHE -ray observations with H.E.S.S. and MAGIC during late May and early June 2016 resulted in the detection of an unprecedented flare, which reveals for the first time VHE -ray intranight variability in this source. While a common variability timescale of 1.5 hr is found, there is a significant deviation near the end of the flare with a timescale of ∼ 20 min marking the cessation of the event. The peak flux is nearly two orders of magnitude above the low-level emission. For the first time, curvature is detected in the VHE -ray spectrum of PKS 1510-089, which is fully explained through absorption by the extragalactic background light. Optical R-band observations with ATOM reveal a counterpart of the -ray flare, even though the detailed flux evolution differs from the VHE lightcurve. Interestingly, a steep flux decrease is observed at the same time as the cessation of the VHE flare. In the high energy (HE, E >100 MeV) -ray band only a moderate flux increase is observed with Fermi-LAT, while the HE -ray spectrum significantly hardens up to a photon index of 1.6. A search for broad-line region (BLR) absorption features in the -ray spectrum indicates that the emission region is located outside of the BLR. Radio VLBI observations reveal a fast moving knot interacting with a standing jet feature around the time of the flare. As the standing feature is located ∼ 50 pc from the black hole, the emission region of the flare may have been located at a significant distance from the black hole. If this correlation is indeed true, VHE rays have been produced far down the jet where turbulent plasma crosses a standing shock.Accepted manuscrip

Selected lectures in microlocal analysis

This paper is a survey of some classical results on microlocal analysis. The first part recalls in particular the notion of analytic wave front set and the theorem of elliptic regularity, along the lines of [M. Sato, T. Kawai and M. Kashiwara, in Hyperfunctions and pseudo-differential equations, 265--529, Lecture Notes in Math., 287, Springer, Berlin, 1973; MR0420735 (54 #8747)] and [L. V. H\uf6rmander, The analysis of linear partial differential operators. I, Grundlehren Math. Wiss., 256, Springer, Berlin, 1983; MR0717035 (85g:35002a)]. The second part deals with propagation of microlocal singularities. It starts with the classical Holmgren uniqueness theorem and proceeds to discuss some variations thereof on propagation at the boundary, where the author has made several contributions

Modifications d'ingestibilité entraînées par la fenaison chez les bovins. Comparaison avec les ovins

International audienc

Conservation et utilisation des spathes de mais par les ruminants. 1. Mise au point d'une technique de conservation et utilisation par les genisses (laitieres et a viande) en croissance, agees de un an, au cours de la periode hivernale

National audienc