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Holomorphic extension of fundamental solutions of elliptic linear partial differential operators of the second order with analytic coefficients. (English) Zbl 1163.35006

Summary: 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 \(\Omega \subset \mathbb R^n\) can be continued at least locally as a multi-valued analytic function in \(\mathbb C^n\) up to the complex bicharacteristic conoid. This extension ramifies or not along its singular set the bicharacteristic conoid and belongs to the Nilsson class.

MSC:

35J15 Second-order elliptic equations
35A08 Fundamental solutions to PDEs
35B60 Continuation and prolongation of solutions to PDEs
32D15 Continuation of analytic objects in several complex variables
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