Nodal set of strongly competition systems with fractional Laplacian

  • Shan Zhang
  • Zuhan LiuEmail author


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.

Mathematics Subject Classification

35Q55 35A05 


Competition system Spatial segregation Free boundary Clean up lemma 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.School of Mathematical ScienceNanjing Normal UniversityNanjingChina
  2. 2.School of Mathematical ScienceYangzhou UniversityYangzhouChina

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