The Edge-of-Wedge Theorem for Systems of Constant Coefficient Partial Differential Operators. II.
The Edge-of-Wedge Theorem for Systems of Constant Coefficient Partial Differential Operators. I.
The overdetermined Cauchy problem
We consider the (characteristic and non-characteristic) Cauchy problem for a system of constant coefficients partial differential equations with initial data on an affine subspace of arbitrary codimension. We show that evolution is equivalent to the validity of a principle on the complex characteristic variety and we study the relationship of this condition with the one introduced by Hörmander in the case of scalar operators and initial data on a hypersurface.
Two symmetry problems in potential theory.