Local approximation of arbitrary functions by solutions of nonlocal equations
Analysis of PDEs
2017-05-24 v4
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 -caloric, up to a small error. The case of non-elliptic and non-parabolic operators is taken into account as well.
Keywords
Cite
@article{arxiv.1609.04438,
title = {Local approximation of arbitrary functions by solutions of nonlocal equations},
author = {Serena Dipierro and Ovidiu Savin and Enrico Valdinoci},
journal= {arXiv preprint arXiv:1609.04438},
year = {2017}
}