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Uniqueness criteria for the adjoint equation in state-constrained elliptic optimal control

Title data

Meyer, Christian ; Panizzi, Lucia ; Schiela, Anton:
Uniqueness criteria for the adjoint equation in state-constrained elliptic optimal control.
In: Numerical Functional Analysis and Optimization. Vol. 32 (2011) Issue 9 . - pp. 983-1007.
ISSN 0163-0563
DOI: https://doi.org/10.1080/01630563.2011.587074

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Project information

Project title:
Project's official titleProject'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 state-constrained optimal control problems. By a counter example of Serrin [18], it is known that, in the presence of non-smooth 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 Boccardo-Galouët [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

Item Type: Article in a journal
Refereed: Yes
Additional notes: A preliminary version is published under the title "Uniqueness criteria for solutions of the adjoint equation in state-constrained optimal control" at the Konrad-Zuse-Zentrum für Informationstechnik, Berlin as ZIB-Report 10-28.
Keywords: elliptical partial differential equations; measure right-hand sides; optimal control; state constraints
Subject classification: Mathematics Subject Classification Code: 35D99 (46N10 49K20)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics) > Professorship Applied Mathematics (Applied Mathematics) - Univ.-Prof. Dr. Anton Schiela
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 13 Mar 2015 08:26
Last Modified: 13 Mar 2015 08:26
URI: https://eref.uni-bayreuth.de/id/eprint/8043