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arXiv · 1607.07704

A note on semilinear fractional elliptic equation: analysis and discretization

Harbir Antil·Johannes Pfefferer·Mahamadi Warma
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Abstract

In this paper we study existence, regularity, and approximation of solution to a fractional semilinear elliptic equation of order $s \in (0,1)$. We identify minimal conditions on the nonlinear term and the source which leads to existence of weak solutions and uniform $L^\infty$-bound on the solutions. Next we realize the fractional Laplacian as a Dirichlet-to-Neumann map via the Caffarelli-Silvestre extension. We introduce a first-degree tensor product finite elements space to approximate the truncated problem. We derive a priori error estimates and conclude with an illustrative numerical example.

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Harbir Antil, Johannes Pfefferer, Mahamadi Warma. 2016-07-21. A note on semilinear fractional elliptic equation: analysis and discretization. https://arxiv.org/abs/1607.07704

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