Higher Hölder regularity for the fractional p-Laplacian in the superquadratic case
By Lorenzo Brasco, Erik Lindgren, Armin Schikorra. Advances in Mathematics, 2017
167 citations recorded by the source corpus.
We prove higher H\"older regularity for solutions of equations involving the fractional $p-$Laplacian of order $s$, when $p\ge 2$ and $0 N/(s\,p)$, which is almost sharp whenever $s\,p\leq (p-1)+N/q$. The result is new already for the homogeneous equation.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/f7fa9e6890681a07f9e6020118c5a65592686564
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In Applied Mathematics
- P. Garain
- Enrico Valdinoci
- Cristiana De Filippis
- Serena Dipierro
- Erik Lindgren
- Giampiero Palatucci
- Juha Kinnunen
- Vicentiu D. Rădulescu
In Computational Theory and Mathematics
- P. Garain
- Enrico Valdinoci
- Serena Dipierro
- Giampiero Palatucci
- Cristiana De Filippis
- Erik Lindgren
- Juha Kinnunen
- E. Vecchi
Citations in the corpus
- A Hong-Krahn-Szegö inequality for mixed local and nonlocal operators (2021, background): “2, we follow the approach in [14]; broadly put, the main idea behind this approach is to transfer to the solution u the oscillation estimates proved in [35] for the Lp,s-harmonic functions.”
- Liouville type theorems and regularity of solutions to degenerate or singular problems part I: even solutions (2019, background): “the first author with Lamboley and Teixeira where they investigate a free boundary problem with a singular weight [14] (see also [15, 16]).”
- Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations (2022, background): “1 to estimate the fractional seminorm [u] W s(p−2− ) p−2 ,q (BR+h0 ) on page 818 in [10].”
- On the regularity theory for mixed local and nonlocal quasilinear elliptic equations (2021, methodology): “We refer to Brasco-Lindgren-Schikorra [10] for tail space and to Garain-Kinnunen [29] for mixed parabolic tail with p = 2.”
- Hölder regularity for nonlocal double phase equations (2019, methodology): “[6] L. Brasco, E. Lindgren, A. Schikorra: Higher Hölder regularity for the fractional pLaplacian in the superquadratic case.”