Letter to the editor.
Linear independence of boundary traces of eigenfunctions of elliptic and Stokes operators and applications
This paper is divided into two parts and focuses on the linear independence of boundary traces of eigenfunctions of boundary value problems. Part I deals with second-order elliptic operators, and Part II with Stokes (and Oseen) operators. Part I: Let be an eigenvalue of a second-order elliptic operator defined on an open, sufficiently smooth, bounded domain Ω in ℝⁿ, with Neumann homogeneous boundary conditions on Γ = tial Ω. Let be the corresponding linearly independent (normalized) eigenfunctions...
Lipschitz stability of optimal controls for the steady-state Navier-Stokes equations
Lipschitz stability of solutions to parametric optimal control problems for parabolic equations.
L∞-Norm minimal control of the wave equation: on the weakness of the bang-bang principle
For optimal control problems with ordinary differential equations where the -norm of the control is minimized, often bang-bang principles hold. For systems that are governed by a hyperbolic partial differential equation, the situation is different: even if a weak form of the bang-bang principle still holds for the wave equation, it implies no restriction on the form of the optimal control. To illustrate that for the Dirichlet boundary control of the wave equation in general not even feasible...
Local quadratic convergence of SQP for elliptic optimal control problems with mixed control-state constraints