Abstract
This paper is concerned with the local structure of the nodal set of segregated configurations associated with a class of fractional singularly perturbed elliptic systems. We prove that the nodal set is a collection of smooth hyper-surfaces, up to a singular set with Hausdorff dimension not greater than n − 2. The proof relies upon a clean-up lemma and the classical dimension reduction principle by Federer.
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15 May 2018
The authors would like to report a mistake in the proof of Theorem 4.1 in [3].
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The work is partially supported by PRC Grant NSFC 11371310, CPSF 2014M551621, and the postdoctoral Research Project of Jiangsu Province 1302043C.
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Zhang, S., Liu, Z. Nodal set of strongly competition systems with fractional Laplacian. Nonlinear Differ. Equ. Appl. 22, 1483–1513 (2015). https://doi.org/10.1007/s00030-015-0332-3
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DOI: https://doi.org/10.1007/s00030-015-0332-3