A link between global solvability and solvability over compacts for systems like :
A Partial Solution of the Pompeiu Problem.
A remark about elliptic overdeterminated systems
A remark on certain overdetermined systems of partial differential equations
A splitting theory for the space of distributions
The splitting problem is studied for short exact sequences consisting of countable projective limits of DFN-spaces (*) 0 → F → X → G → 0, where F or G are isomorphic to the space of distributions D'. It is proved that every sequence (*) splits for F ≃ D' iff G is a subspace of D' and that, for ultrabornological F, every sequence (*) splits for G ≃ D' iff F is a quotient of D'
A symmetry result for a fourth order overdetermined boundary value problem.
An Approximation Theorem for Integrable Harmonic Vector Fields.
An elementary theory of hyperfunctions and microfunctions
An inverse Neumann problem.
Boundary regularity and compactness for overdetermined problems
Let be either the unit ball or the half ball let be a strictly positive and continuous function, and let and solve the following overdetermined problem:where denotes the characteristic function of denotes the set and the equation is satisfied in the...
Caratterizzazione dei sistemi ipoellittici a coefficienti costanti, sovradeterminati, con il metodo della paramatrice
Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives
This paper is an extended version of an invited talk presented during the Orlicz Centenary Conference (Poznań, 2003). It contains a brief survey of applications to classical problems of analysis of the theory of the so-called PLS-spaces (in particular, spaces of distributions and real analytic functions). Sequential representations of the spaces and the theory of the functor Proj¹ are applied to questions like solvability of linear partial differential equations, existence of a solution depending...
Evoluzione per sistemi differenziali sovradeterminati
Localization and wave fronts
On a Bernoulli problem with geometric constraints
A Bernoulli free boundary problem with geometrical constraints is studied. The domain Ω is constrained to lie in the half space determined by x1 ≥ 0 and its boundary to contain a segment of the hyperplane {x1 = 0} where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition simultaneously on the free boundary. The existence and uniqueness of a solution have already been addressed...
On a Bernoulli problem with geometric constraints
A Bernoulli free boundary problem with geometrical constraints is studied. The domain Ω is constrained to lie in the half space determined by x1 ≥ 0 and its boundary to contain a segment of the hyperplane {x1 = 0} where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition simultaneously on the free boundary. The existence and uniqueness of a solution have already been addressed...
On some conjectures by E. De Giorgi relative to the global resolvability of overdetermined systems of differential equations
Overdetermined hyperbolic systems on l.e. convex sets
Partial differential analogs of ordinary differential equations and systems.
Schiffer problem and isoparametric hypersurfaces.
The Schiffer Problem as originally stated for Euclidean spaces (and later for some symmetric spaces) is the following: Given a bounded connected open set Ω with a regular boundary and such that the complement of its closure is connected, does the existence of a solution to the Overdetermined Neumann Problem (N) imply that Ω is a ball? The same question for the Overdetermined Dirichlet Problem (D). We consider the generalization of the Schiffer problem to an arbitrary Riemannian manifold and also...