Title data
Meyer, Christian ; Panizzi, Lucia ; Schiela, Anton:
Uniqueness criteria for the adjoint equation in stateconstrained elliptic optimal control.
In: Numerical Functional Analysis and Optimization.
Vol. 32
(2011)
Issue 9
.
 pp. 9831007.
ISSN 01630563
DOI: https://doi.org/10.1080/01630563.2011.587074
Project information
Project title: 
Project's official title  Project's id 

DFG Research Center Matheon "Mathematics for key technologies"  FZT 86 

Project financing: 
Deutsche Forschungsgemeinschaft

Abstract in another language
The article considers linear elliptic equations with regular Borel measures as inhomogeneity. Such equations frequently appear in stateconstrained optimal control problems. By a counter example of Serrin [18], it is known that, in the presence of nonsmooth data, a standard weak formulation does not ensure uniqueness for such equations. Therefore several notions of solution have been developed that guarantee uniqueness. In this note, we compare different definitions of solutions, namely the ones of Stampacchia [19] and BoccardoGalouët [4] and the two notions of solutions of [2, 7], and show that they are equivalent. As side results, we reformulate the solution in the sense of [19], and prove the existence of solutions in the sense of [2, 4, 7] in case of mixed boundary conditions.
Further data