2010/06/03 by Yong‐Cheol Kim, Yong-Cheol Kim, Kim, Yong-Cheol +2
Economics, Econometrics and Finance · Mathematics · #35B65 #35D10 (60J75) #35J60 #45K05 #47G20 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stochastic processes and financial applications #math.AP #math.CA #msc:35B65 #msc:35D10 #msc:35J60 #msc:45K05 #msc:47G20
paper · pdf · doi:10.48550/arxiv.1006.0608
openalex publication_date 2010/06/03 · arxiv created 2010/10/29 · arxiv updated 2010/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new class of fully nonlinear integro-differential operators with possible nonsymmetric kernels, which includes the ones that arise from stochastic control problems with purely jump Lèvy processes. If the index of the operator σ is in (1,2) (subcritical case), then we obtain a comparison principle, a nonlocal version of the Alexandroff-Backelman-Pucci estimate, a Harnack inequality, a Hölder regularity, and an interior \rm C1,α-regularity for fully nonlinear integro-differential equations associated with such a class. Moreover, our estimates remain uniform as the index σ of the operator is getting close to two, so that they can be regarded as a natural extension of regularity results for elliptic partial differential equations.