We study the regularity of solutions of elliptic fractional systems of order 2s,
@article{AIHPC_2019__36_1_165_0, author = {Caffarelli, Luis and D\'avila, Gonzalo}, title = {Interior regularity for fractional systems}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {165--180}, publisher = {Elsevier}, volume = {36}, number = {1}, year = {2019}, doi = {10.1016/j.anihpc.2018.04.004}, mrnumber = {3906869}, zbl = {1411.35111}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2018.04.004/} }
TY - JOUR AU - Caffarelli, Luis AU - Dávila, Gonzalo TI - Interior regularity for fractional systems JO - Annales de l'I.H.P. Analyse non linéaire PY - 2019 SP - 165 EP - 180 VL - 36 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2018.04.004/ DO - 10.1016/j.anihpc.2018.04.004 LA - en ID - AIHPC_2019__36_1_165_0 ER -
%0 Journal Article %A Caffarelli, Luis %A Dávila, Gonzalo %T Interior regularity for fractional systems %J Annales de l'I.H.P. Analyse non linéaire %D 2019 %P 165-180 %V 36 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2018.04.004/ %R 10.1016/j.anihpc.2018.04.004 %G en %F AIHPC_2019__36_1_165_0
Caffarelli, Luis; Dávila, Gonzalo. Interior regularity for fractional systems. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 1, pp. 165-180. doi : 10.1016/j.anihpc.2018.04.004. http://archive.numdam.org/articles/10.1016/j.anihpc.2018.04.004/
[1] Regularity theorems for weak solutions of some nonlinear systems, Commun. Pure Appl. Math., Volume 35 (1982) no. 6, pp. 833–838 | DOI | MR | Zbl
[2] Regularity theory for fully nonlinear integro-differential equations, Commun. Pure Appl. Math., Volume 62 (2009) no. 5, pp. 597–638 | MR | Zbl
[3] The Evans–Krylov theorem for nonlocal fully nonlinear equations, Ann. Math. (2011) no. 2, pp. 1163–1187 | MR | Zbl
[4] Fractional harmonic maps into manifolds in odd dimension
[5] Three-term commutator estimates and the regularity of 1/2-harmonic maps into spheres, Anal. PDE, Volume 4 (2011) no. 1, pp. 149–190 | MR | Zbl
[6] Sub-criticality of non-local Schrödinger systems with antisymmetric potentials and applications to half-harmonic maps, Adv. Math., Volume 227 (2011) no. 3, pp. 1300–1348 | DOI | MR | Zbl
[7]
[8] Nonlocal Harnack inequalities, J. Funct. Anal., Volume 267 (15 September 2014) no. 6, pp. 1807–1836 | DOI | MR | Zbl
[9] Hitchhiker's guide to the fractional Sobolev spaces, Bull. Sci. Math., Volume 136 (2012) no. 5, pp. 521–573 | MR | Zbl
[10] An existence theorem for harmonic mappings of Riemannian manifolds, Acta Math., Volume 138 (1977) no. 1–2, pp. 1–16 | MR | Zbl
[11] On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order, Ann. Sc. Norm. Super. Pisa, Cl. Sci., Volume 4 (1977), pp. 145–178 | Numdam | MR | Zbl
[12] On regularity for Beurling–Deny type Dirichlet forms, Potential Anal., Volume 19 (August 2003) no. 1, pp. 69–87 | DOI | MR | Zbl
[13] M. Kassmann, Harnack inequalities and Hölder regularity estimates for nonlocal operators revisited, available as SFB 701-preprint no. 11015, 2011.
[14] On a fractional Ginzburg–Landau equation and 1/2-harmonic maps into spheres, Arch. Ration. Mech. Anal., Volume 215 (2015) no. 1, pp. 125–210 | MR | Zbl
[15] Regularity of
[16] Integro-differential harmonic maps into spheres, Commun. Partial Differ. Equ., Volume 40 (2015) no. 3, pp. 506–539 (English summary) | DOI | MR | Zbl
[17] ε-regularity for systems involving non-local, antisymmetric operators, Calc. Var. Partial Differ. Equ., Volume 54 (2015) no. 4, pp. 3531–3570 (English summary) | DOI | MR | Zbl
[18]
[19] Ein optimaler Regularitätssatz für schwache Lösungen gewisser elliptischer Systeme, Math. Z., Volume 147 (1976) no. 1, pp. 21–28 | MR | Zbl
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