Higher Hölder regularity for fractional $(p,q)$-Laplace equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908608679116800 |
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| author | Garain, Prashanta Lindgren, Erik |
| author_facet | Garain, Prashanta Lindgren, Erik |
| contents | We study the fractional $(p,q)$-Laplace equation $$ (-Δ_p)^s u +(-Δ_q)^t u= 0 $$ for $s,t\in(0,1)$ and $p,q\in(1,\infty)$. We establish Hölder estimates with an explicit exponent. As a consequence, we derive a Liouville-type theorem. Our approach builds on techniques previously developed for the fractional $p$-Laplace equation, relying on a Moser-type iteration for difference quotients. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_15988 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher Hölder regularity for fractional $(p,q)$-Laplace equations Garain, Prashanta Lindgren, Erik Analysis of PDEs We study the fractional $(p,q)$-Laplace equation $$ (-Δ_p)^s u +(-Δ_q)^t u= 0 $$ for $s,t\in(0,1)$ and $p,q\in(1,\infty)$. We establish Hölder estimates with an explicit exponent. As a consequence, we derive a Liouville-type theorem. Our approach builds on techniques previously developed for the fractional $p$-Laplace equation, relying on a Moser-type iteration for difference quotients. |
| title | Higher Hölder regularity for fractional $(p,q)$-Laplace equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.15988 |