Pseudodifferential parametrices of infinite order for SG-hyperbolic problems.
Pseudodifferenziali definiti su aperti di una cosfera fibrata
Pseudo-spectrum for a class of semi-classical operators
We study in this paper a notion of pseudo-spectrum in the semi-classical setting called injectivity pseudo-spectrum. The injectivity pseudo-spectrum is a subset of points in the complex plane where there exist some quasi-modes with a precise rate of decay. For that reason, these values can be considered as some ‘almost eigenvalues’ in the semi-classical limit. We are interested here in studying the absence of injectivity pseudo-spectrum, which is characterized by a global a priori estimate. We prove...
Pseudospectrum for differential operators
Quantification asymptotique et microlocalisations d'ordre supérieur
Quantification relativiste
Rational invariant tori, phase space tunneling, and spectra for non-selfadjoint operators in dimension
We study spectral asymptotics and resolvent bounds for non-selfadjoint perturbations of selfadjoint -pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part is completely integrable. Spectral contributions coming from rational invariant Lagrangian tori are analyzed. Estimating the tunnel effect between strongly irrational (Diophantine) and rational tori, we obtain an accurate description of the spectrum in a suitable complex window, provided that the...
Recent development in the theory of linear partial differential equations.
Recent progress in the regularity theory of Fourier integrals with real and complex phases and solutions to partial differential equations
In this paper we will give a brief survey of recent regularity results for Fourier integral operators with complex phases. This will include the case of real phase functions. Applications include hyperbolic partial differential equations as well as non-hyperbolic classes of equations. An application to an oblique derivative problem is also given.
Réduction microlocale des systèmes d'opérateurs pseudo-différentiels
On sait depuis 1976 qu’il existe un lien entre systèmes de champs de vecteurs réels et groupes nilpotents. On montre ici que ce phénomène s’étend aux systèmes d’opérateurs pseudo-différentiels à symboles principaux réels. Une équivalence de propriétés est conjecturée, mais seule l’une des implications est ici démontrée.
Régularité des solutions des équations aux dérivées partielles non linéaires
Régularité lipschitzienne et solutions de l'équation des ondes sur une variété riemannienne compacte
Régularité microlocale pour des problèmes aux limites non linéaires
Regularity for Signorini's Problem in linear eleasticity.
Regularity up to the boundary of solutions of the Dirichlet problem for certain degenerate elliptic equations.
Remainder estimates for eigenvalues and kernels of pseudo-differential elliptic systems.
Remarks on Gårding inequalities for differential operators
Classical Gårding inequalities such as those of Hörmander, Hörmander-Melin or Fefferman-Phong are proved by pseudo-differential methods which do not allow to keep a good control on the supports of the functions under study nor on the smoothness of the coefficients of the operator. In this paper, we show by very simple calculations that in certain special situations, the results that can be obtained directly are much better than those expected thanks to the general theory.
Remarques sur le caractère algébrique du procédé pseudo-différentiel et de certaines de ses extensions (I)
Représentation des fonctions de BMO et solutions dé l'équation ...b.
Résolubilité et hypoellipticité de systèmes surdéterminés