Caratterizzazione dei polinomi di convoluzione in una variabile a decrescenza rapida, a coefficienti costanti, che hanno soluzioni quasi periodiche per ogni termine noto quasi periodico
Caratterizzazione dei sistemi ipoellittici a coefficienti costanti, sovradeterminati, con il metodo della paramatrice
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...
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...
Completely semielliptic boundary value problems
Concavity properties of solutions to some degenerate quasilinear elliptic Dirichlet problems
Constant Coefficient Differential Operators with Slowly Spreading Solutions.
Continuous linear right inverses for partial differential operators of order 2 and fundamental solutions in half spaces.
Diffraction pour l'équation de la chaleur
Diffusion phenomenon for second order linear evolution equations
We present an abstract theory of the diffusion phenomenon for second order linear evolution equations in a Hilbert space. To derive the diffusion phenomenon, a new device developed in Ikehata-Matsuyama [5] is applied. Several applications to damped linear wave equations in unbounded domains are also given.
Dimension reduction for functionals on solenoidal vector fields
We study integral functionals constrained to divergence-free vector fields in Lp on a thin domain, under standard p-growth and coercivity assumptions, 1 < p < ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in Lp is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject to the limiting constraint...
Dimension reduction for functionals on solenoidal vector fields
We study integral functionals constrained to divergence-free vector fields in Lp on a thin domain, under standard p-growth and coercivity assumptions, 1 < p < ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in Lp is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject to the limiting constraint...
Division Problem and Partial Differential Equations with Constant Coefficients in Colombeau's Space of New Generalized Functions.
Estimates for Green's matrices of elliptic systems by Lp theory.
Explicit solution for Lamé and other PDE systems
We provide a general series form solution for second-order linear PDE system with constant coefficients and prove a convergence theorem. The equations of three dimensional elastic equilibrium are solved as an example. Another convergence theorem is proved for this particular system. We also consider a possibility to represent solutions in a finite form as partial sums of the series with terms depending on several complex variables.
Exponentiation de la dérivation, et intégration des séries en variables non commutatives
Extension and lacunas of solutions of linear partial differential equations
Let be compact, convex sets in with and let be a linear, constant coefficient PDO. It is characterized in various ways when each zero solution of in the space of all -functions on extends to a zero solution in resp. in . The most relevant characterizations are in terms of Phragmén-Lindelöf conditions on the zero variety of in and in terms of fundamental solutions for with lacunas.
Extension of formal power series solutions
Extension of zero-solutions of partial differential operators with dominating principal part.
First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods
In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial...