Two problems on approximation by solutions of elliptic systems on compact sets in the plane

Abstract

Motivated by recent results by M. Mazalov about uniform approximation of functions by solutions of elliptic equations with constant complex coefficients we study two problems on approximation of functions by solutions of general homogeneous elliptic second-order systems of partial differential equations. The approximation is considered in spaces of continuous and -functions on compact sets in the complex plane.

Keywords:

• Second-order elliptic system
• uniform approximation
• -approximation

AMS Subject Classifications:

• Primary: 30E10
• Secondary: 35J47

Acknowledgements

A part of this work was done in January–February 2017 during a “research in pairs” meeting at the CIRM (Luminy), France. Another part of this work was done during the Simons Semester “Emergent trends of Complex Analysis and Functional Analysis” hosted by IMPAN, Poland. The author thanks the CIRM and IMPAN for their hospitality.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

The work was supported by the Russian Science Foundation [project number 17-11-01064].