## View abstract

### Session S18 - Recent progress in non-linear PDEs and their applications

Tuesday, July 20, 17:00 ~ 17:50 UTC-3

## Gamma convergence and asymptotic behavior for eigenvalues of nonlocal problems

### Julian Fernandez Bonder

#### University of Buenos Aires, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak29e2e26b327ed622d2d86ef64e54fd76').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy29e2e26b327ed622d2d86ef64e54fd76 = 'jfb&#111;nd&#101;r' + '&#64;'; addy29e2e26b327ed622d2d86ef64e54fd76 = addy29e2e26b327ed622d2d86ef64e54fd76 + 'dm' + '&#46;' + '&#117;b&#97;' + '&#46;' + '&#97;r'; var addy_text29e2e26b327ed622d2d86ef64e54fd76 = 'jfb&#111;nd&#101;r' + '&#64;' + 'dm' + '&#46;' + '&#117;b&#97;' + '&#46;' + '&#97;r';document.getElementById('cloak29e2e26b327ed622d2d86ef64e54fd76').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy29e2e26b327ed622d2d86ef64e54fd76 + '\'>'+addy_text29e2e26b327ed622d2d86ef64e54fd76+'<\/a>';

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 $p-$fractional laplacian when the fractional parameter $s$ goes to 1, and to extend some known results for the behavior of the same eigenvalue problem when $p$ goes to $\infty$. Finally we analyze other eigenvalue problems not previously covered in the literature. This is a joint work with A. Silva and J. Spedaletti from UNSL-Argentina.