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/
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