A Dirichlet problem of the fractional Laplace equation in the bounded Lipschitz domain

2012/05/22 by Chang, Tongkeun
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1205.4814

Abstract

In this paper, we study a Dirichlet problem of a fractional Laplace equation in a bounded Lipschitz domain in \R, n ≥ 2. Our main result is that for the given data F ∈ H^s(\Om^c), 0 < s<1, we find the function which satisfies that \De^s u =0 in \Om, u|_\Om^c =F and |u|_H^s(\R) ≤ c |F| _H^s(\Om^c). Furthermore, we represent the solution with an integral operator.

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