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 $L u = g(x,u)\qquad\text{in }Ω$ with an elliptic operator $L$ of $2m$ order with variable coefficients and a Carathéodory function $g:Ω\times \mathbb{C}\to\mathbb{C}$, where $Ω\subset\mathbb{R}^N$ is an open set with $N > 2m$.

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