Schauder estimates for solutions of linear parabolic integro-differential equations
Tianling Jin, Jingang Xiong
TL;DR
This paper establishes optimal Schauder and Hölder estimates for solutions of linear parabolic integro-differential equations, advancing the understanding of their regularity properties in space and time.
Contribution
It provides the first optimal pointwise Schauder estimates and Hölder regularity results for solutions of these equations.
Findings
Optimal pointwise Schauder estimates in space.
Optimal Hölder estimates in space-time.
Enhanced regularity understanding for linear parabolic integro-differential equations.
Abstract
We prove optimal pointwise Schauder estimates in the spatial variables for solutions of linear parabolic integro-differential equations. Optimal H\"older estimates in space-time for those spatial derivatives are also obtained.
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