TY - GEN A1 - Tröltzsch, Fredi A1 - Yousept, Irwin T1 - Source representation strategy for optimal boundary control problems with state constraints N2 - A state-constrained optimal boundary control problem governed by a linear elliptic equation is considered. In order to obtain the optimality conditions for the solutions to the model problem, a Slater assumption has to be made that restricts the theory to the two-dimensional case. This difficulty is overcome by a source representation of the control and combined with a Lavrentiev type regularization. Optimality conditions for the regularized problem are derived, where the corresponding Lagrange multipliers have $L^2$-regularity. By the spectral theorem for compact and normal operators, the convergence result is shown. Moreover, the convergence for vanishing regularization parameter of the adjoint state associated with the regularized problem is shown. Finally, the uniform boundedness of the regularized Lagrange multipliers in $L^1(\O)$ is verified by a maximum principle argument. Y1 - 2007 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/393 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-3930 ER -