Anti-symmetry of the second eigenfunction of the fractional Laplace operator in a 3-D ball

  • Rui A. C. FerreiraEmail author


In this work we extend a recent result by Dyda et al. (J Lond Math Soc 95(2):500–518, 2017) to dimension 3.


Fractional Laplacian Anti-symmetry Unit ball 

Mathematics Subject Classification

Primary 35P15 35R11 



The author would like to thank Professor Pedro Antunes for fruitful discussions on the problem. The author is also grateful for the kind email-reply of Professors Dyda, Kuznetsov and Kwaśnicki.


  1. 1.
    Bañuelos, R., Kulczycki, T.: The Cauchy process and the Steklov problem. J. Funct. Anal. 211(2), 355–423 (2004)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bucur, C., Valdinoci, E.: Nonlocal diffusion and applications. Lecture Notes of the Unione Matematica Italiana, vol. 20. Springer (2016)Google Scholar
  3. 3.
    Dragomir, S.S., Agarwal, R.P., Barnett, N.S.: Inequalities for beta and gamma functions via some classical and new integral inequalities. J. Inequal. Appl. 5(2), 103–165 (2000)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Dyda, B., Kuznetsov, A., Kwaśnicki, M.: Eigenvalues of the fractional Laplace equation in the unit ball. J. Lond. Math. Soc. 95(2), 500–518 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Kwaśnicki, M.: Eigenvalues of the fractional Laplace operator in the interval. J. Funct. Anal. 262(5), 2379–2402 (2012)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Grupo Física-Matemática, Faculdade de CiênciasUniversidade de LisboaLisboaPortugal

Personalised recommendations