2,833 research outputs found
Finite element approximation for the fractional eigenvalue problem
The purpose of this work is to study a finite element method for finding
solutions to the eigenvalue problem for the fractional Laplacian. We prove that
the discrete eigenvalue problem converges to the continuous one and we show the
order of such convergence. Finally, we perform some numerical experiments and
compare our results with previous work by other authors.Comment: 20 pages, 6 figure
Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics
We show for a certain class of operators and holomorphic functions
that the functional calculus is holomorphic. Using this result
we are able to prove that fractional Laplacians depend real
analytically on the metric in suitable Sobolev topologies. As an
application we obtain local well-posedness of the geodesic equation for
fractional Sobolev metrics on the space of all Riemannian metrics.Comment: 31 page
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