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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.10034 |
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| _version_ | 1866914166952951808 |
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| author | Gan, Ziyu Jiao, Heming |
| author_facet | Gan, Ziyu Jiao, Heming |
| contents | In [1], Caffarelli-Charro introduced a fractional Monge-Ampère 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10034 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Locally uniform ellipticity of the fractional Hessian operators Gan, Ziyu Jiao, Heming Analysis of PDEs In [1], Caffarelli-Charro introduced a fractional Monge-Ampère 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. |
| title | Locally uniform ellipticity of the fractional Hessian operators |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.10034 |