Analysis & PDE

  • Anal. PDE
  • Volume 9, Number 3 (2016), 727-772.

Regularity for parabolic integro-differential equations with very irregular kernels

Russell W. Schwab and Luis Silvestre

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We prove Hölder regularity for a general class of parabolic integro-differential equations, which (strictly) includes many previous results. We present a proof that avoids the use of a convex envelope as well as give a new covering argument that is better suited to the fractional order setting. Our main result involves a class of kernels that 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.

Article information

Anal. PDE, Volume 9, Number 3 (2016), 727-772.

Received: 3 October 2015
Accepted: 16 December 2015
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47G20: Integro-differential operators [See also 34K30, 35R09, 35R10, 45Jxx, 45Kxx] 35R09: Integro-partial differential equations [See also 45Kxx]

nonlocal equations nonsymmetric kernels covering lemma crawling ink spots regularity


Schwab, Russell W.; Silvestre, Luis. Regularity for parabolic integro-differential equations with very irregular kernels. Anal. PDE 9 (2016), no. 3, 727--772. doi:10.2140/apde.2016.9.727.

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