Regular oblique derivative problem in Morrey spaces

Abstract

This article presents a study of the regular oblique derivative problem $$ displaylines{ sum_{i,j=1}^n a^{ij}(x) frac{partial^2 u }{partial x_ipartial x_j} =f(x) cr frac{partial u }{partial ell(x)}+ sigma(x) u = varphi(x),. }$$ Assuming that the coefficients $a^{ij}$ belong to the Sarason's class of functions with vanishing mean oscillation, we show existence and global regularity of strong solutions in Morrey spaces.

Keywords

• Uniformly elliptic operator
• regular oblique derivative problem
• Morrey spaces.