Volume 38_2_(2017)_277-290

Fundamental solutions of second order elliptic linear partial differential operators with analytic coefficients and simple complex characteristics
SERGE LUKASIEWICZ

Abstract. We give an explicit formula for the fundamental solutions of an elliptic linear partial differential operator of the second order with analytic coefficients and simple complex characteristics in an open set Ω ⊂ Rn. We prove that those fundamental solutions can be continued at least locally as multi-valued analytic functions x → E(x, y) in Cn up to the complex bicharacteristic conoid. This extension ramifies along its singular set the bicharacteristic conoid and belongs to the Nilsson class

Rend. Mat. Appl. (7) 38 (2017) 277-290;  pdf