Brezis--Kato Type Regularity Results for Higher Order Elliptic Operators

Abstract

We prove a Brezis--Kato regularity type results for solutions of the higher order nonlinear elliptic equation \[ L u = g(x,u)\qquad\text{in }Ω\] with an elliptic operator $L$ of $2m$ order with variable coefficients and a Carathéodory function $g:\Omega \times \mathbb{C}\to \mathbb{C}$, where $\Omega \subset {\mathbb{R}}^N$ is an open set with $N>2m$.