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

Jakub Siemianowski

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arXiv · 2202.11408

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

Jakub Siemianowski

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Abstract

We prove a Brezis--Kato regularity type results for solutions of the higher order nonlinear elliptic equation \[ L u = g(x,u)\qquad\text{in }\Omega \] 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 $N > 2m$.

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Jakub Siemianowski. 2022-02-23. Brezis--Kato Type Regularity Results for Higher Order Elliptic Operators. https://arxiv.org/abs/2202.11408

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