A lower closure theorem for abstract control problems withL p-bounded controls

1974 ◽  
Vol 14 (5) ◽  
pp. 521-528 ◽  
Author(s):  
L. D. Berkovitz
Keyword(s):  
Control Problems ◽  
Closure Theorem ◽  
Bounded Controls ◽  
Lower Closure ◽  
Lower Closure Theorem

A lower closure theorem for autonomous orientor fields

1988 ◽  
Vol 110 (3-4) ◽  
pp. 249-254 ◽  
Author(s):  
Luigi Ambrosio
Keyword(s):  
Differential Inclusion ◽  
Closure Property ◽  
Closure Theorem ◽  
Set Valued Mapping ◽  
Orientor Fields ◽  
Lower Closure ◽  
Lower Closure Theorem ◽  
Image Position

SynopsisGiven a set valued mapping ∑: ℝ → ∑n, we prove a closure property with respect to -convergence for the differential inclusionunder very mild assumptions on ∑.

scholarly journals Optimal Control of a Nonlinear PDE Governed by Fractional Laplacian

2021 ◽  
Author(s):  
Rafał Kamocki
Keyword(s):  
Optimal Control ◽  
Fractional Laplacian ◽  
Nonlinear Pde ◽  
Optimal Solutions ◽  
Dirichlet Laplacian ◽  
Existence Of Optimal Solutions ◽  
Closure Theorem ◽  
Orientor Fields ◽  
Lower Closure ◽  
Lower Closure Theorem

AbstractWe consider an optimal control problem containing a control system described by a partial nonlinear differential equation with the fractional Dirichlet–Laplacian, associated to an integral cost. We investigate the existence of optimal solutions for such a problem. In our study we use Filippov’s approach combined with a lower closure theorem for orientor fields.

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