Estimates for nondivergence elliptic equations with VMO coefficients in generalized grand Morrey spaces

Abstract

In this paper, we establish the regularity, in generalized grand Morrey spaces, of the solution to elliptic equations in non-divergence form with VMO coefficients by means of the theory of singular integrals and linear commutators.

Keywords:

• elliptic equation
• Morrey spaces
• VMO
• singular integrals
• commutators

AMS Subject Classifications:

• 35J25
• 42B20

Acknowledgments

The first and second named authors were partially supported by the Shota Rustaveli National Science Foundation with Grant (Project numbers D/13-23 and 31/47). The third named author was partially supported by Pontificia Universidad Javeriana, Research Project Elliptic Equations in Grand Morrey spaces ID PRY: 005779. We would like to thank the anonymous referee for helpful comments.