TY - GEN A1 - Hömberg, Dietmar A1 - Krumbiegel, Klaus A1 - Rehberg, Joachim T1 - Boundary coefficient control - A maximal parabolic regularity approach N2 - We investigate a control problem for the heat equation. The goal is to find an optimal heat transfer coefficient in the Robin boundary condition such that a desired temperature distribution at the boundary is adhered. To this end we consider a function space setting in which the heat flux across the boundary is forced to be an Lp function with respect to the surface measure, which in turn implies higher regularity for the time derivative of temperature. We show that the corresponding elliptic operator generates a strongly continuous semigroup of contractions and apply the concept of maximal parabolic regularity. This allows to show the existence of an optimal control and the derivation of necessary and sufficient optimality conditions. KW - parabolic equation KW - mixed boundary condition KW - maximal parabolic Lp-regularity KW - optimal control KW - sufficient optimality conditions Y1 - 2011 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/805 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-8056 ER -