@article {ipa|Quantitative estimates on localised finite differences for the fractional Poisson problem, and applications to regularity and spectral stability|2017,
	title = {Quantitative estimates on localised finite differences for the fractional Poisson problem, and applications to regularity and spectral stability},
	year = {2017},
	month = {January},
	pages = {38 p.},
	institution = {CNR-IMATI},
	type = {Working paper},
	address = {Pavia},
	abstract = {<p>We establish new quantitative estimates for localized finite differences of solutions to the Poisson problem for the fractional Laplace operator with homogeneous Dirichlet conditions of solid type settled in bounded domains satisfying the Lipschitz cone regularity condition. We then apply these estimates to obtain (i) regularity results for solutions of fractional Poisson problems in Besov spaces; (ii) quantitative stability estimates for solutions of fractional Poisson problems with respect to domain perturbations; (iii) quantitative stability estimates for eigenvalues and eigenfunctions of fractional Laplace operators with respect to domain perturbations.</p>
},
	keywords = {Spectral stability},
	url = {http://irs.imati.cnr.it/reports/irs17-03},
	author = {G. Akagi and G. Schimperna and A. Segatti and L.V. Spinolo}
}
