THE SECOND EIGENVALUE OF THE FRACTIONAL p − LAPLACIAN

@inproceedings{Brasco2015THESE,
  title={THE SECOND EIGENVALUE OF THE FRACTIONAL p − LAPLACIAN},
  author={Lorenzo Brasco and Enea Parini},
  year={2015}
}
We consider the eigenvalue problem for the fractional p−Laplacian in an open bounded, possibly disconnected set Ω ⊂ R, under homogeneous Dirichlet boundary conditions. After discussing some regularity issues for eigenfuctions, we show that the second eigenvalue λ2(Ω) is welldefined, and we characterize it by means of several equivalent variational formulations. In particular, we extend the mountain pass characterization of Cuesta, De Figueiredo and Gossez to the nonlocal and nonlinear setting… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 27 references

On an inequality concerning the eigenvalue problem of membrane

I. Hong
Kōdai Math. Sem. Rep., 6 • 1954
View 11 Excerpts
Highly Influenced

Über Minimaleigenschaften der Kugel in drei und mehr Dimensionen

E. Krahn
Acta Comm. Univ. Dorpat., A9 • 1926
View 13 Excerpts
Highly Influenced

Nonlocal equations with measure data

T. Kuusi, G. Mingione, Y. Sire
preprint • 2014
View 8 Excerpts
Highly Influenced

Fractional eigenvalues

E. Lindgren, P. Lindqvist
Calc. Var. Partial Differential Equations, 49 • 2014
View 3 Excerpts

Fractional p − eigenvalues , Riv

G. Palatucci G. Franzina
2014

Fractional p−eigenvalues

G. Franzina, G. Palatucci
Riv. Mat. Univ. Parma, 5 • 2014
View 1 Excerpt

Local behavior of fractional p−minimizers

A. Di Castro, T. Kuusi, G. Palatucci
preprint • 2014
View 1 Excerpt

Nonlocal Harnack inequalities

A. Di Castro, T. Kuusi, G. Palatucci
J. Funct. Anal., 267 • 2014
View 1 Excerpt

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