Gamma convergence and asymptotic behavior for eigenvalues of nonlocal problems
Julián Fernández Bonder, Analía Silva, Juan F. Spedaletti · Discrete and Continuous Dynamical Systems · 2020
In this paper we analyze the asymptotic behavior of several fractional eigenvalue problems by means of Gamma-convergence methods. This method allows us to treat different eigenvalue problems under a unified framework. We are able to recover some known results for the behavior of the eigenvalues of the \begin{document}$ p- $\end{document} fractional laplacian when the fractional parameter \begin{document}$ s $\end{document} goes to 1, and to extend some known results for the behavior of the same eigenvalue problem when \begin{document}$ p $\end{document} goes to \begin{document}$ \infty $\end{document} . Finally we analyze other eigenvalue problems not previously covered in the literature.