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arXiv · 2604.01665

Analyticity up to the boundary for the divergence equation

Igor Kukavica·Qi Xu
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Abstract

We address analytic regularity for the divergence equation $\text{div}\, u = f$ in $\Omega$, with $u=0$ on $\partial\Omega$, where $\Omega$ is an arbitrary bounded analytic domain and $\int_{\Omega} f\,dx=0$. If $f$ is analytic on the closure of $\Omega$, then we prove that there exists a solution that is analytic on the closure of $\Omega$.

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Igor Kukavica, Qi Xu. 2026-04-02. Analyticity up to the boundary for the divergence equation. https://arxiv.org/abs/2604.01665

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