Mathematical Research Letters

Volume 23 (2016)

Number 4

An integro-differential equation without continuous solutions

Pages: 1157 – 1166

DOI: https://dx.doi.org/10.4310/MRL.2016.v23.n4.a9

Authors

Luis Silvestre (Department of Mathematics, University of Chicago, Illinois, U.S.A.)

Stanley Snelson (Department of Mathematics, University of Chicago, Illinois, U.S.A.)

Abstract

We show an example of a non symmetric integro-differential equation of order $\alpha$, for $\alpha \in (0, 1)$, for which Hölder estimates do not hold even though the kernels are comparable to the fractional Laplacian.

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Accepted 5 February 2016

Published 16 September 2016