Viene studiata l'equazione per le forme regolari sulla chiusura dell'intersezione di domini pseudoconvessi. Si costruisce un operatore soluzione in forma integrale e sotto ipotesi opportune si ottengono stime della soluzione nelle norme .
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.
We consider the solution operator to the -operator restricted to forms with coefficients in . Here denotes -forms with coefficients in , is the corresponding -space and is a suitable rotation-invariant absolutely continuous finite measure. We will develop a general solution formula to . This solution operator will have the property . As an application of the solution formula we will be able to characterize compactness of the solution operator in terms of compactness of commutators...
The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately to obstructions to the existence of solutions. Moreover, we will deduce that the solution space of such equations is always finite dimensional.
We derive formulas for the values in the interior of the L2-minimal solutions of the ∂∂-equation in the unit ball of Cn. These formulas generalize previously known formulas for the boundary values of the same solutions. We estimate the solution and obtain a (known) result concerning weighted Nevanlinna classes.