Publication Date:
2016-06-09
Description:
The paper 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, 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 and the two notions of solutions of Casas and Alibert-Raymond, and show that they are the same. As side results, we reformulate the solution
in the sense of Stampacchia, and prove the existence and uniqueness of solutions in
in case of mixed boundary conditions.
Language:
English
Type:
reportzib
,
doc-type:preprint
Format:
application/pdf
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