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arXiv · 1412.3790

Regularity for parabolic integro-differential equations with very irregular kernels

Russell W. Schwab·Luis Silvestre
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Abstract

We prove Hölder regularity for a general class of parabolic integro-differential equations, which (strictly) includes many previous results. We present a proof which avoids the use of a convex envelop as well as give a new covering argument which is better suited to the fractional order setting. Our main result involves a class of kernels which may contain a singular measure, may vanish at some points, and are not required to be symmetric. This new generality of integro-differential operators opens the door to further applications of the theory, including some regularization estimates for the Boltzmann equation.

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Russell W. Schwab, Luis Silvestre. 2014-12-11. Regularity for parabolic integro-differential equations with very irregular kernels. https://doi.org/10.2140/apde.2016.9.727

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