Local solvability of PDE with constant coefficients
Localizations of partial differential operators and surjectivity on real analytic functions
Let P(D) be a partial differential operator with constant coefficients which is surjective on the space A(Ω) of real analytic functions on an open set . Then P(D) admits shifted (generalized) elementary solutions which are real analytic on an arbitrary relatively compact open set ω ⊂ ⊂ Ω. This implies that any localization of the principal part is hyperbolic w.r.t. any normal vector N of ∂Ω which is noncharacteristic for . Under additional assumptions must be locally hyperbolic.
Locally Cogent Boundary Operators.
Nonexistence of a Continuous Right Inverse for Linear Partial Differential Operators with Constant Coefficients.
Nonlinear perturbations of systems of partial differential equations with constant coefficients.
On a mixed problem for a constant coefficient second-order system.
On algebraic characterization of coercive linear partial differential operators with constant coefficients
On tensor functions whose gradients have some skew-symmetries
Let be a real inner product space of any dimension; and let be a -map relating any two tensor spaces on . We study the consequences imposed on the form of this function by the condition that its gradient should be skew-symmetric with respect to some pairs of indexes. Any such a condition is written as a system of linear partial differential equations, with constant coefficients, which is symmetric with respect to certain couples of independent variables. The solutions of these systems appear...
On the Functional Dimension of Solution Spaces of Hypoelliptic Partial Differential Operators.
On the functors Ext¹(E,F) for Fréchet spaces
On the "Fundamental Principle" of L. Ehrenpreis
On the Influence of Lower Order Terms for Propagation of Analytic Singularities for Operators with Constant Coefficients.
Overdetermined hyperbolic systems on l.e. convex sets
Partial Differential Equations without Solution Operators in Weighted Spaces of (Generalized) Functions.
Quelques résultats sur la résolubilité analytique des équations linéaires à coefficients constants
Régularité Gevrey et itérés pour une classe d'opérateurs hypoelliptiques
Résolubilité Gevrey d'opérateurs différentiels à coefficients constants
Si discute l'esistenza di soluzioni su insiemi aperti per equazioni differenziali iperbolico-ipoellittiche. Si dà una caratterizzazione geometrica quasi completa per aperti .
Right inverses for partial differential operators on Fourier hyperfunctions
We characterize the partial differential operators P(D) admitting a continuous linear right inverse in the space of Fourier hyperfunctions by means of a dual (Ω̅)-type estimate valid for the bounded holomorphic functions on the characteristic variety near . The estimate can be transferred to plurisubharmonic functions and is equivalent to a uniform (local) Phragmén-Lindelöf-type condition.
Risoluzione di una congettura di De Giorgi in
Sistemi del tipo non globalmente risolubili