Local approximation of arbitrary functions by solutions of nonlocal equations

2016/09/14 by Dipierro, Serena, Savin, Ovidiu, Valdinoci, Enrico · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.04438

Abstract

We show that any function can be locally approximated by solutions of prescribed linear equations of nonlocal type. In particular, we show that every function is locally s-caloric, up to a small error. The case of non-elliptic and non-parabolic operators is taken into account as well.

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