no. 5
Schauder estimates for nonlocal fully nonlinear equations
Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 5, pp. 1375-1407.

In this paper, we establish pointwise Schauder estimates for solutions of nonlocal fully nonlinear elliptic equations by perturbative arguments. A key ingredient is a recursive Evans–Krylov theorem for nonlocal fully nonlinear translation invariant equations.

DOI : 10.1016/j.anihpc.2015.05.004
Classification : 35R09, 35B65
Mots clés : Integro-differential equations, Schauder estimates, Recursive Evans–Krylov theorem 
@article{AIHPC_2016__33_5_1375_0,
     author = {Jin, Tianling and Xiong, Jingang},
     title = {Schauder estimates for nonlocal fully nonlinear equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1375--1407},
     publisher = {Elsevier},
     volume = {33},
     number = {5},
     year = {2016},
     doi = {10.1016/j.anihpc.2015.05.004},
     zbl = {1349.35386},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2015.05.004/}
}
TY  - JOUR
AU  - Jin, Tianling
AU  - Xiong, Jingang
TI  - Schauder estimates for nonlocal fully nonlinear equations
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2016
SP  - 1375
EP  - 1407
VL  - 33
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2015.05.004/
DO  - 10.1016/j.anihpc.2015.05.004
LA  - en
ID  - AIHPC_2016__33_5_1375_0
ER  - 
%0 Journal Article
%A Jin, Tianling
%A Xiong, Jingang
%T Schauder estimates for nonlocal fully nonlinear equations
%J Annales de l'I.H.P. Analyse non linéaire
%D 2016
%P 1375-1407
%V 33
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2015.05.004/
%R 10.1016/j.anihpc.2015.05.004
%G en
%F AIHPC_2016__33_5_1375_0
Jin, Tianling; Xiong, Jingang. Schauder estimates for nonlocal fully nonlinear equations. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 5, pp. 1375-1407. doi : 10.1016/j.anihpc.2015.05.004. http://www.numdam.org/articles/10.1016/j.anihpc.2015.05.004/

[1] Barles, G.; Chasseigne, E.; Imbert, C. Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations, J. Eur. Math. Soc., Volume 13 (2011), pp. 1–26 | Zbl

[2] Barrera, B.; Figalli, A.; Valdinoci, E. Bootstrap regularity for integro-differential operators, and its application to nonlocal minimal surfaces, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5), Volume 13 (2014), pp. 609–639

[3] Bass, R.F. Regularity results for stable-like operators, J. Funct. Anal., Volume 257 (2009), pp. 2693–2722 | Zbl

[4] Caffarelli, L.A. Interior a priori estimates for solutions of fully nonlinear equations, Ann. Math. (2), Volume 130 (1989), pp. 189–213 | DOI | Zbl

[5] Caffarelli, L.A.; Cabré, X. Fully Nonlinear Elliptic Equations, Am. Math. Soc. Colloq. Publ., vol. 43, American Mathematical Society, Providence, RI, 1995 | Zbl

[6] Caffarelli, L.A.; Silvestre, L. Regularity theory for fully nonlinear integro-differential equations, Commun. Pure Appl. Math., Volume 62 (2009), pp. 597–638 | DOI | Zbl

[7] Caffarelli, L.A.; Silvestre, L. Regularity results for nonlocal equations by approximation, Arch. Ration. Mech. Anal., Volume 200 (2011), pp. 59–88 | DOI | Zbl

[8] Caffarelli, L.A.; Silvestre, L. The Evans–Krylov theorem for non local fully non linear equations, Ann. Math. (2), Volume 174 (2011), pp. 1163–1187 | DOI | Zbl

[9] Chang Lara, H.A.; Davila, G. Regularity for solutions of non local parabolic equations, Calc. Var. Partial Differ. Equ., Volume 49 (2014), pp. 139–172 | Zbl

[10] Chang Lara, H.A.; Davila, G. Regularity for solutions of non local parabolic equations II, J. Differ. Equ., Volume 256 (2014), pp. 130–156 | DOI

[11] Chang Lara, H.A.; Davila, G. Hölder estimates for non-local parabolic equations with critical drift | arXiv | DOI | Zbl

[12] Chang Lara, H.A.; Davila, G. Cσ+α estimates for concave, non-local parabolic equations with critical drift | arXiv | Zbl

[13] Dong, H.; Kim, D. On Lp-estimates for a class of nonlocal elliptic equations, J. Funct. Anal., Volume 262 (2012) no. 3, pp. 1166–1199 | DOI | Zbl

[14] Dong, H.; Kim, D. Schauder estimates for a class of non-local elliptic equations, Discrete Contin. Dyn. Syst., Volume 33 (2013), pp. 2319–2347 | DOI | Zbl

[15] Guillen, N.; Schwab, R.W. Aleksandrov–Bakelman–Pucci type estimates for integro-differential equations, Arch. Ration. Mech. Anal., Volume 206 (2012) no. 1, pp. 111–157 | DOI | Zbl

[16] Jin, T.; Xiong, J. Schauder estimates for solutions of linear parabolic integro-differential equations | arXiv | DOI | Zbl

[17] Kassmann, M.; Rang, M.; Schwab, R.W. Hölder regularity for integro-differential equations with nonlinear directional dependence, Indiana Univ. Math. J., Volume 63 (2014), pp. 1467–1498

[18] Kriventsov, D. C1,α interior regularity for nonlinear nonlocal elliptic equations with rough kernels, Commun. Partial Differ. Equ., Volume 38 (2013), pp. 2081–2106 | DOI | Zbl

[19] Ladyzenskaja, O.A.; Solonnikov, V.A.; Ural'ceva, N.N. Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monogr., vol. 23, American Mathematical Society, Providence, RI, 1968 (translated from the Russian by S. Smith) | DOI | Zbl

[20] Li, Y.Y.; Nirenberg, L. Estimates for elliptic system from composition material, Commun. Pure Appl. Math., Volume 56 (2003), pp. 892–925 | Zbl

[21] Mikulevicius, R.; Pragarauskas, H. On the Cauchy problem for integro-differential operators in Hölder classes and the uniqueness of the martingale problem, Potential Anal., Volume 40 (2014) no. 4, pp. 539–563 | DOI | Zbl

[22] Ros-Oton, X.; Serra, J. Boundary regularity for fully nonlinear integro-differential equations | arXiv | DOI | Zbl

[23] Serra, J. Regularity for fully nonlinear nonlocal parabolic equations with rough kernels | arXiv | DOI | Zbl

[24] Serra, J. Cσ+α regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels | arXiv | DOI | Zbl

[25] L. Silvestre, Personal communications.

Cité par Sources :