Higher Hölder regularity for the fractional $p$-Laplace equation in the subquadratic case
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911893199781888 |
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| author | Garain, Prashanta Lindgren, Erik |
| author_facet | Garain, Prashanta Lindgren, Erik |
| contents | We study the fractional $p$-Laplace equation $$ (-Δ_p)^s u = 0 $$ for $0<s<1$ and in the subquadratic case $1<p<2$. We provide Hölder estimates with an explicit Hölder exponent. The inhomogeneous equation is also treated and there the exponent obtained is almost sharp. Our results complement the previous results for the superquadratic case when $p\geq 2$. The arguments are based on a careful Moser-type iteration and a perturbation argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03600 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Higher Hölder regularity for the fractional $p$-Laplace equation in the subquadratic case Garain, Prashanta Lindgren, Erik Analysis of PDEs We study the fractional $p$-Laplace equation $$ (-Δ_p)^s u = 0 $$ for $0<s<1$ and in the subquadratic case $1<p<2$. We provide Hölder estimates with an explicit Hölder exponent. The inhomogeneous equation is also treated and there the exponent obtained is almost sharp. Our results complement the previous results for the superquadratic case when $p\geq 2$. The arguments are based on a careful Moser-type iteration and a perturbation argument. |
| title | Higher Hölder regularity for the fractional $p$-Laplace equation in the subquadratic case |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2310.03600 |