A link between and analytic solvability for P.D.E. with constant coefficients
A sufficient condition for existence of real analytic solutions of P.D.E. with constant coefficients, in open sets of
Characterization of surjective partial differential operators on spaces of real analytic functions
Let A(Ω) denote the real analytic functions defined on an open set Ω ⊂ ℝⁿ. We show that a partial differential operator P(D) with constant coefficients is surjective on A(Ω) if and only if for any relatively compact open ω ⊂ Ω, P(D) admits (shifted) hyperfunction elementary solutions on Ω which are real analytic on ω (and if the equation P(D)f = g, g ∈ A(Ω), may be solved on ω). The latter condition is redundant if the elementary solutions are defined on conv(Ω). This extends and improves previous...
Concavity properties of solutions to some degenerate quasilinear elliptic Dirichlet problems
On the condition of Λ-convexity in some problems of weak continuity and weak lower semicontinuity
We study the functional , where u=(u₁, ..., uₘ) and each is constant along some subspace of ℝⁿ. We show that if intersections of the ’s satisfy a certain condition then is weakly lower semicontinuous if and only if f is Λ-convex (see Definition 1.1 and Theorem 1.1). We also give a necessary and sufficient condition on to have the equivalence: is weakly continuous if and only if f is Λ-affine.
On the envelope of regularity for solutions of homogeneous systems of linear partial differential operators
On the global solvability of linear partial differential equations with constant coefficients in the space of real analytic functions
This article surveys results on the global surjectivity of linear partial differential operators with constant coefficients on the space of real analytic functions. Some new results are also included.
Ouverts concaves et théorèmes de dualité pour les systèmes différentiels à coefficients constants
Problema di Cauchy semiglobale in due variabili
Problèmes de convexité pour les opérateurs différentiels à coefficients constants
Proximinality and co-proximinality in metric linear spaces
As a counterpart to best approximation, the concept of best coapproximation was introduced in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, this study was taken up by many researchers. In this paper, we discuss some results on the existence and uniqueness of best approximation and best coapproximation when the underlying spaces are metric linear spaces
Qualitative properties of solutions to elliptic singular problems.
Surjectivity of partial differential operators on ultradistributions of Beurling type in two dimensions
We show that if Ω is an open subset of ℝ², then the surjectivity of a partial differential operator P(D) on the space of ultradistributions of Beurling type is equivalent to the surjectivity of P(D) on .
The surjectivity of a constant coefficient homogeneous differential operator in the real analytic functions and the geometry of its symbol
Hörmander has characterized the surjective constant coefficient partial differential operators on the space of all real analytic functions on by a Phragmén-Lindelöf condition. Geometric implications of this condition and, for homogeneous operators, of the corresponding condition for Gevrey classes are given.
Un teorema sui polinomi differenziali omogenei in
Критерий локальной разрешимости уравнений в частных производных с постоянными коэффициентами