Geodesic
Regularity theory for nonlocal equations with VMO coefficients
Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 1, pp. 61-132

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We prove higher regularity for nonlinear nonlocal equations with possibly discontinuous coefficients of VMO type in fractional Sobolev spaces. While for corresponding local elliptic equations with VMO coefficients it is only possible to obtain higher integrability, in our nonlocal setting we are able to also prove a substantial amount of higher differentiability, so that our result is in some sense of purely nonlocal type. By embedding, we also obtain higher Hölder regularity for such nonlocal equations.

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Publié le :
DOI : 10.4171/aihpc/37
Classification : 35R09, 35B65, 35D30, 46E35, 47G20
Keywords: Nonlocal operator, nonlocal equations, Sobolev regularity, Calderón–Zygmund estimates, Hölder regularity 
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     author = {Nowak, Simon},
     title = {Regularity theory for nonlocal equations with {VMO} coefficients},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {61--132},
     volume = {40},
     number = {1},
     year = {2023},
     doi = {10.4171/aihpc/37},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/37/}
}
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Nowak, Simon. Regularity theory for nonlocal equations with VMO coefficients. Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 1, pp. 61-132. doi: 10.4171/aihpc/37

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