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Dini and Schauder estimates for nonlocal fully nonlinear parabolic equations with drifts. (English) Zbl 1392.35048

Summary: We obtain Dini- and Schauder-type estimates for concave fully nonlinear nonlocal parabolic equations of order \(\sigma\in (0,2)\) with rough and nonsymmetric kernels and drift terms. We also study such linear equations with only measurable coefficients in the time variable, and obtain Dini-type estimates in the spacial variable. This is a continuation of work by the authors Dong and Zhang.

MSC:

35B45 A priori estimates in context of PDEs
35K55 Nonlinear parabolic equations
35R09 Integro-partial differential equations
35B65 Smoothness and regularity of solutions to PDEs
60J75 Jump processes (MSC2010)
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[1] 10.4153/CJM-2002-042-9 · Zbl 1112.35037 · doi:10.4153/CJM-2002-042-9
[2] 10.1016/0022-0396(78)90003-7 · Zbl 0362.35021 · doi:10.1016/0022-0396(78)90003-7
[3] 10.1002/cpa.20274 · Zbl 1170.45006 · doi:10.1002/cpa.20274
[4] 10.4007/annals.2011.174.2.9 · Zbl 1232.49043 · doi:10.4007/annals.2011.174.2.9
[5] 10.1007/BF02415082 · Zbl 0144.14101 · doi:10.1007/BF02415082
[6] 10.1002/cpa.21671 · Zbl 1365.35194 · doi:10.1002/cpa.21671
[7] 10.1016/j.jfa.2011.11.002 · Zbl 1232.35182 · doi:10.1016/j.jfa.2011.11.002
[8] 10.3934/dcds.2013.33.2319 · Zbl 1263.45008 · doi:10.3934/dcds.2013.33.2319
[9] 10.1007/s00013-002-8217-1 · Zbl 1013.35028 · doi:10.1007/s00013-002-8217-1
[10] 10.3934/dcds.2015.35.5977 · Zbl 1334.35370 · doi:10.3934/dcds.2015.35.5977
[11] 10.1016/j.anihpc.2015.05.004 · Zbl 1349.35386 · doi:10.1016/j.anihpc.2015.05.004
[12] 10.1007/s00208-013-0948-8 · Zbl 1283.47054 · doi:10.1007/s00208-013-0948-8
[13] 10.1007/BF00284620 · Zbl 0468.35014 · doi:10.1007/BF00284620
[14] 10.2969/jmsj/03630387 · Zbl 0539.60081 · doi:10.2969/jmsj/03630387
[15] 10.1080/03605309708821325 · Zbl 0899.35036 · doi:10.1080/03605309708821325
[16] 10.1090/gsm/012 · doi:10.1090/gsm/012
[17] 10.1007/s00526-012-0576-2 · Zbl 1292.35068 · doi:10.1007/s00526-012-0576-2
[18] 10.1007/s11401-017-1079-4 · Zbl 1367.35055 · doi:10.1007/s11401-017-1079-4
[19] 10.1007/BF01774284 · Zbl 0658.35050 · doi:10.1007/BF01774284
[20] ; Lieberman, Differential Integral Equations, 5, 1219 (1992) · Zbl 0785.35047
[21] 10.1016/j.jde.2010.06.023 · Zbl 1225.35070 · doi:10.1016/j.jde.2010.06.023
[22] 10.1007/BF02450422 · Zbl 0795.45007 · doi:10.1007/BF02450422
[23] 10.1007/s11118-013-9359-4 · Zbl 1296.45009 · doi:10.1007/s11118-013-9359-4
[24] 10.1016/j.jde.2016.02.006 · Zbl 1336.35350 · doi:10.1016/j.jde.2016.02.006
[25] ; Nirenberg, Contributions to the theory of partial differential equations. Annals of Mathematics Studies, 33, 95 (1954) · Zbl 0057.08604
[26] ; Safonov, Izv. Akad. Nauk SSSR Ser. Mat., 52, 1272 (1988)
[27] 10.2140/apde.2016.9.727 · Zbl 1349.47079 · doi:10.2140/apde.2016.9.727
[28] 10.1007/s00526-015-0914-2 · Zbl 1344.35042 · doi:10.1007/s00526-015-0914-2
[29] 10.1007/BF02384477 · Zbl 0506.35028 · doi:10.1007/BF02384477
[30] 10.1007/s11401-006-0142-3 · Zbl 1151.35329 · doi:10.1007/s11401-006-0142-3
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