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Corpus ID: 227238825

Comparison principles for a class of nonlinear non-local integro-differential operators on unbounded domains.

@article{Ladas2020ComparisonPF,
title={Comparison principles for a class of nonlinear non-local integro-differential operators on unbounded domains.},
author={Nikolaos Michael Ladas and J. C. Meyer},
journal={arXiv: Analysis of PDEs},
year={2020}
}

We present extensions of the comparison and maximum principles available for nonlinear non-local integro-differential operators $P:\mathcal{C}^{2,1}(\Omega \times (0,T])\times L^\infty (\Omega \times (0,T])\to\mathbb{R}$, of the form $P[u] = L[u] -f(\cdot ,\cdot ,u,Ju)$ on $\Omega \times (0,T]$. Here, we consider: unbounded spatial domains $\Omega \subset \mathbb{R}^n$, with $T>0$; sufficiently regular second order linear parabolic partial differential operators $L$; sufficiently regular semi… Expand