Some remarks on existence results for optimal boundary control problems
Universidad de Castilla-La Mancha, 13071 Ciudad
Real, Spain; Pablo.Pedregal@uclm.es.
Revised: 17 October 2002
An optimal control problem when controls act on the boundary can also be understood as a variational principle under differential constraints and no restrictions on boundary and/or initial values. From this perspective, some existence theorems can be proved when cost functionals depend on the gradient of the state. We treat the case of elliptic and non-elliptic second order state laws only in the two-dimensional situation. Our results are based on deep facts about gradient Young measures.
Mathematics Subject Classification: 49J20 / 49J45
Key words: Boundary controls / vector variational problems / gradient Young measures.
© EDP Sciences, SMAI, 2003