• Corpus ID: 239024771

# Existence of solutions for nonlinear elliptic PDEs with fractional Laplacians on open balls

@inproceedings{Penent2021ExistenceOS,
title={Existence of solutions for nonlinear elliptic PDEs with fractional Laplacians on open balls},
author={Guillaume Penent and Nicolas Privault},
year={2021}
}
• Published 19 October 2021
• Mathematics
We prove the existence of viscosity solutions for fractional semilinear elliptic PDEs on open balls with bounded exterior condition in dimension d ≥ 1. Our approach relies on a tree-based probabilistic representation based on a (2s)-stable branching processes for all s ∈ (0, 1), and our existence results hold for sufficiently small exterior conditions and nonlinearity coefficients. In comparison with existing approaches, we consider a wide class of polynomial nonlinearities without imposing…
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