# Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation

Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient... Let $$L=\Delta ^{\alpha /2}+ b\cdot \nabla$$ with $$\alpha \in (1,2)$$ . We prove the Martin representation and the Relative Fatou Theorem for non-negative singular L-harmonic functions on $$\mathcal{C }^{1,1}$$ bounded open sets. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation

, Volume 17 (4) – Jan 8, 2013
28 pages

/lp/springer_journal/martin-representation-and-relative-fatou-theorem-for-fractional-iwM7dehsdr
Publisher
Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-012-0220-6
Publisher site
See Article on Publisher Site

### Abstract

Let $$L=\Delta ^{\alpha /2}+ b\cdot \nabla$$ with $$\alpha \in (1,2)$$ . We prove the Martin representation and the Relative Fatou Theorem for non-negative singular L-harmonic functions on $$\mathcal{C }^{1,1}$$ bounded open sets.

### Journal

PositivitySpringer Journals

Published: Jan 8, 2013

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