Elliptic operators of divergence type with Hölder coefficients in fractional Sobolev spaces

Abstract

This work concerns linear elliptic operators of divergence type with Hölder coefficients in spaces of type W^{1+s}_p (Ω), s ∈ [0, 1[ on a Lipschitz domain Ω. We prove that if the Laplace operator ∆ is a bicontinuous isomorphism from W^{1+s}_p (Ω) onto W^{s−1}_p (Ω) then the result holds for more general elliptic operators with Hölder coefficients. An application to a non linear problem with low regularity in the right-hand side is given.

Keywords

• hölder coefficients
• elliptic operator
• interpolation
• fractional sobolev spaces