Das Poincarésche Randsteuerproblem bei elliptischen Differentialgleichungen zweiter Ordnung. (The Poincaré boundary control problem for elliptic differential equations of second order) (Q1063854)

Riemann-Hilbert control problems of the form \[ \quad \delta_{\bar z}W+A(z,v(z))W+B(z,v(z))\bar W=F(z,v(z))\quad in\quad G \] \[ \quad a(t,u(t))Re W(t)+b(t,u(t))Im W(t)\equiv Re[\overline{\lambda (t,u(t))W}]=c(t,u(t)) \] with additional constraints and integral cost functional and Poincaré boundary control problems of the form \[ \quad \Delta \omega +A(x,y)\omega_ x+B(x,y)\omega_ y+\alpha C(x,y)\omega =F(x,y)\quad in\quad G \] \[ a(t,u(t))\omega_ x-b(t,u(t))\omega_ y+\alpha c(t,u(t))\omega =f(t,u(t))\quad on\quad \Gamma =\partial G \] with additional constraints and integral cost functional are considered. The paper refers to some existence results regarding these two problems.