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On a new Kato class and positive solutions of Dirichlet problems for the fractional Laplacian in bounded domains. (English) Zbl 1209.31005
Summary: The purpose of this paper is to extend some results of potential theory for elliptic operators to the fractional Laplacian $(-\Delta)^{\alpha /2}$, $0<\alpha <2$, in a bounded $C^{1,1}$ domain $D$ in $\Bbb R^n$. In particular, we introduce a new Kato class $K_{\alpha} (D)$, and we exploit the properties of this class to study the existence of positive solutions of some Dirichlet problems for the fractional Laplacian.

31C99Generalizations in potential theory
Full Text: DOI
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