Some topics on the regularity of analytic-Gevrey vectors


  • Makhlouf Derridj 5, Rue de la Juviniére, 78350 Les Loges en Josas, France



Microlocal regularity, Gevrey vectors, Degenerate elliptic-parabolic differential operators


My aim is to give, in this talk, some topics on the question of regularity of Analytic-Gevrey vectors of partial differential operators (p.d.o.) with analytic-Gevrey coefficients. Since the results obtained in the sixties on elliptic p.d.o's, which are both hypoelliptic (C setting), analytic-Gevrey hypoelliptic (analytic-Gevrey setting) and satisfy the so-called Kotake-Narasimhan property, a lot of works and articles were devoted to these problems in case of non elliptic p.d.o's under suitable hypotheses (for example on the degeneracy of ellipticity). I will consider the third problem on analytic-Gevrey vectors in the three cases of global (on compact manifolds), local (near a point in the base-space), microlocal (near a point in the cotangent space), situations, and say few words on the main two methods used in order to obtain positive (or negative) results. Finally I will focus on some new microlocal results on degenerate elliptic (also called sub-elliptic) p.d.o's of second order, obtained in a common work with Gregorio Chinni.




How to Cite

Derridj, M. (2024). Some topics on the regularity of analytic-Gevrey vectors. Bruno Pini Mathematical Analysis Seminar, 14(2), 77–100.