Paolo Acquistapace

On BMO Regularity for Linear Elliptic Systems (

SummaryWe prove a refinement of Campanatos result on local and global (under Dirichlet boundary conditions) BMO regularity for the gradient of solutions of linear elliptic systems of second order in divergence form: we just need that the coefficients are «small multipliers of BMO(Ω)», a class neither containing, nor contained in

Infinite-horizon linear-quadratic regulator problems for nonautonomous parabolic systems with boundary control

C^0 \left( {\bar \Omega } \right)

A Theory of the Infinite Horizon LQ-Problem for Composite Systems of PDEs with Boundary Control

. We also prove local and global Lp regularity: this result neither implies, nor follows by the classical one by Agmon, Douglis and Nirenberg.

Γ-Convergence for Infinite Dimensional Optimal Control Problems

Abstract We study existence, uniqueness and regularity of the strict, classical and strong solutions uϵ C(¦0, T ¦,E) of the non-autonomous evolution equation u′(t) − A(t)u(t)=ƒ(t) , with the initial datum u(0) = x, in a Banach space E, under the classical Kato-Tanabe assumptions. The domains of the operators A(t) are not needed to be dense in E. We prove necessary and sufficient conditions for existence and Holder regularity of the solution and its derivative.

Mathematical Phase Model of Neural Populations Interaction in Modulation of REM/NREM Sleep

This paper concerns the classical linear-quadratic regulator problem for general nonautonomous parabolic systems with boundary control over infinite time horizon from the point of view of semigroup theory. Under appropriate assumptions we prove existence and uniqueness of the optimal pair, as well as existence, uniqueness, and further properties of the solution of the associated Riccati equation. Several examples are discussed in detail.

Minimum energy for linear systems with finite horizon: a non-standard Riccati equation

The linear non-autonomous evolution equation u’(t) -A(t) u(t) =f(t), t E [0, T], with the initial datum u(O) =x, in the space C([O, T], E), where E is a Banach space and (A(t)} is a family of infinitesimal generators of bounded analytic semigroups is considered; the domains D@(t)) are supposed constant in t and possibly not dense in E. Maximal regularity of the strict and classical solutions, i.e., regularity of u’ and A(.)u(.) with values in the interpolation spaces D,,O,(l?, co) and DA&B) between D@(O)) and E, is studied. A characterization of such spaces in a concrete case is also given. 0 1985 Academic Press, Inc.

A unified approach to abstract linear non-autonomous parabolic equations

We study the infinite horizon linear-quadratic (LQ) problem and the associated algebraic Riccati equations for systems with unbounded control actions. The operator-theoretic context is motivated by composite systems of partial differential equations (PDEs) with boundary or point control. Specific focus is placed on systems of coupled hyperbolic/parabolic PDE with an overall “predominant” hyperbolic character, such as, e.g., some models for thermoelastic or fluid-structure interactions. While unbounded control actions lead to Riccati equations with unbounded (operator) coefficients, unlike in the parabolic case solvability of these equations becomes a major issue, owing to the lack of sufficient regularity of the solutions to the composite dynamics. In the present case, even the more general theory appealing to estimates of the singularity displayed by the kernel which occurs in the integral representation of the solution to the control system fails. A novel framework which embodies possible hyperbolic com...

Evolution operators and strong solutions of abstract linear parabolic equations

Among the general goals in the various theories of variational convergence, an important one consists in singling out a notion of Γ-limit problem (P) for a sequence of minimum problems (P n ) of the form