A global characteristic of g‐limit operators for quasilinear potential elliptic systems¹

This research was partially supported by the Latvian Council of Sciences, Grant No. 01.0441.

Abstract

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.

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.

Key words:

• elliptic systems
• convex functions
• G‐limit operators

Notes

This research was partially supported by the Latvian Council of Sciences, Grant No. 01.0441.