34 research outputs found
A note on semilinear fractional elliptic equation: analysis and discretization
In this paper we study existence, regularity, and approximation of solution
to a fractional semilinear elliptic equation of order . We
identify minimal conditions on the nonlinear term and the source which leads to
existence of weak solutions and uniform -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