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2011 A duality approach to the fractional Laplacian with measure data
Kenneth H. Karlsen, Francesco Petitta, Suleyman Ulusoy
Publ. Mat. 55(1): 151-161 (2011).

Abstract

We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems like

$$(-\Delta)^s v = \mu \quad \text{in } \mathbb{R}^N,$$

with vanishing conditions at infinity. Here $\mu$ is a bounded Radon measure whose support is compactly contained in $\mathbb{R}^N$, $N\geq2$, and $-(\Delta)^s$ is the fractional Laplace operator of order $s\in (1/2,1)$.

Citation

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Kenneth H. Karlsen. Francesco Petitta. Suleyman Ulusoy. "A duality approach to the fractional Laplacian with measure data." Publ. Mat. 55 (1) 151 - 161, 2011.

Information

Published: 2011
First available in Project Euclid: 25 February 2011

zbMATH: 1208.35162
MathSciNet: MR2779579

Subjects:
Primary: 35B40, 35K55

Rights: Copyright © 2011 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.55 • No. 1 • 2011
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