A global characteristic of g‐limit operators for quasilinear potential elliptic systems

The paper considers a family of quasilinear potential elliptic systems and uses the fact that all G‐limit operators for this family can be characterized by means of gradients of convex functions F (locally with respect to the spatial co‐ordinates). It is shown that all these functions F must satisfy an inequality expressed in terms of functions F and their conjugate functions. G-ribinių operatorių globalioji charakteristika kvazitiesinėms potencinėms elipsinėms sistemoms Santrauka Straipsnyje nagrinejama kvazitiesiniu potenciniu elipsiniu sistemu šeima ir pasinaudojama, kad visi G‐ribiniai operatoriai šiai šeimai gali būti charakterizuojami iškiliosios funkcijos F gradiento (lokaliai erdviniu koordinačiu atžvilgiu) reikšmemis. Parodyta, kad visos šios funkcijos F tenkina nelygybe, išreikšta per funkcijas F ir joms jungtines funkcijas. First Published Online: 14 Oct 201

Counterexample to extension via convexification of optimal control problems for elliptic systems

We present a counterexample, which shows that convexification, i.e. the passage to the convex hull of the set of admissible operators, does not preserve the convex hull of the set of feasible states of the corresponding family of elliptic systems