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

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