Locally uniform ellipticity of the fractional Hessian operators

Ziyu Gan; Heming Jiao

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arXiv · 2511.10034

Locally uniform ellipticity of the fractional Hessian operators

Ziyu Gan·Heming Jiao

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Abstract

In [1], Caffarelli-Charro introduced a fractional Monge-Amp\`{e}re operator. Later, Wu [17] generalized it to a fractional analogue of $k$-Hessian operators and proved the strict ellipticity for $k=2$. In this paper, we introduce a fractional analogue of general Hessian operators and prove the stability. We also show that the fractional analogue $k$-Hessian operators defined in [17] are strictly elliptic with respect to convex solutions for all $2 \leq k \leq n$. Furthermore, we provide a new proof for the case $k=2$ without the convexity condition.

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Ziyu Gan, Heming Jiao. 2025-11-13. Locally uniform ellipticity of the fractional Hessian operators. https://arxiv.org/abs/2511.10034

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