Abstract
We obtain Schauder estimates for a general class of linear integro-differential equations. The estimates are applied to a scalar non-local Burgers equation and complete the global well-posedness results obtained in [6].
Highlights
This note studies the classical Schauder estimates for a general class of linear integro-differential equations of the form m(t, x, y) wt(t, x) = p.v. (w(t, Rn y) −w(t, x)) |x y|n+1 dy. (1.1)Cyril Imbert, Tianling Jin and Roman ShvydkoyWe assume that m ∈ Cα((−6, 0] × Rn × Rn), λ m Λ, and w ∈ C1+α((−6, 0] × Rn), for some α > 0, λ, Λ > 0
The regularity theory of fully nonlinear integro-differential equations in non-divergence form was developed before in Caffarelli–Silvestre [2], and Lara–Dávila [9]. This implies the Cα-regularity of m for solutions bounded away from zero
We summarize the result in the following
Summary
Article mis en ligne dans le cadre du Centre de diffusion des revues académiques de mathématiques http://www.cedram.org/
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Annales de la Faculté des sciences de Toulouse : Mathématiques
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
