User's guide to the fractional Laplacian and the method of semigroups

2018/08/15 by Stinga, P. R. · 7 citations
#26A33 #35R11 #58J35 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1808.05159

Abstract

The method of semigroups is a unifying, widely applicable, general technique to formulate and analyze fundamental aspects of fractional powers of operators L and their regularity properties in related functional spaces. The approach was introduced by the author and José L.~Torrea in 2009 (arXiv:0910.2569v1). The aim of this chapter is to show how the method works in the particular case of the fractional Laplacian L^s=(-Δ)^s, 0

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