Holomorphic extension of fundamental solutions of elliptic linear partial differential operators of the second order with analytic coefficients

摘要

We prove that every fundamental solution of an elliptic linear partial differential operator of the second order with analytic coefficients and simple complex characteristics in an open set Omega subset of R-n can be continued at least locally as a multi-valued analytic function in C-n up to the complex bicharacteristic conoid. This extension ramifies or not along its singular set the bicharacteristic conoid and belongs to the Nilsson class. To cite this article: S. Lukasiewicz, C. R. Acad. Sci. Paris, Ser. I 347 (2009).