Abstract:
In this paper, we study an optimal shape design problem for the first eigenvalue of the fractional p-Laplacian with mixed boundary conditions. The optimization variable is the set where the Dirichlet condition is imposed (that is restricted to have measure equal to a prescribed quantity α). We show existence of an optimal design and analyze the asymptotic behavior when the fractional parameter s converges to 1, and thus obtain asymptotic bounds that are independent of α. © 2018 Walter de Gruyter GmbH, Berlin/Boston 2018.
Registro:
Documento: |
Artículo
|
Título: | Optimal Design Problems for the First p-Fractional Eigenvalue with Mixed Boundary Conditions |
Autor: | Fernández Bonder, J.; Rossi, J.D.; Spedaletti, J.F. |
Filiación: | Departamento de Matemática FCEN, Universidad de Buenos Aires, IMAS-CONICET, Ciudad Universitaria, Pabellón i (C1428EGA), Av. Cantilo 2160, Buenos Aires, Argentina Departamento de Matemática, Universidad Nacional de San Luis, IMASL-CONICET, Ejército de los Andes 950, San Luis, D5700HHW, Argentina
|
Palabras clave: | Fractional Laplacian; Gamma Convergence; Shape Optimization |
Año: | 2018
|
Volumen: | 18
|
Número: | 2
|
Página de inicio: | 323
|
Página de fin: | 335
|
DOI: |
http://dx.doi.org/10.1515/ans-2018-0001 |
Título revista: | Advanced Nonlinear Studies
|
Título revista abreviado: | Adv. Nonlinear Stud.
|
ISSN: | 15361365
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v18_n2_p323_FernandezBonder |
Referencias:
- Bourgain, J., Brezis, H., Mironescu, P., Another look at Sobolev spaces (2001) Optimal Control and Partial Differential Equations. in Honour of Professor Alain Bensoussan's 60th Birthday, pp. 439-455. , IOS Press, Amsterdam
- Brasco, L., Parini, E., Squassina, M., Stability of variational eigenvalues for the fractional p-Laplacian (2016) Discrete Contin. Dyn. Syst., 36 (4), pp. 1813-1845
- Bucur, D., Buttazzo, G., Variational Methods in some Shape Optimization Problems (2002) Appunti Corsi Tenuti Docenti Sc., Scuola Normale Superiore, Pisa
- Bucur, D., Trebeschi, P., Shape optimisation problems governed by nonlinear state equations (1998) Proc. Roy. Soc. Edinb. Sect. A, 128 (5), pp. 945-963
- Chanillo, S., Grieser, D., Imai, M., Kurata, K., Ohnishi, I., Symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes (2000) Comm. Math. Phys., 214 (2), pp. 315-337
- Di Nezza, E., Palatucci, G., Valdinoci, E., Hitchhiker's guide to the fractional Sobolev spaces (2012) Bull. Sci. Math., 136 (5), pp. 521-573
- Fernández Bonder, J., Spedaletti, J.F., Some nonlocal optimal design problems (2018) J. Math. Anal. Appl., 459 (2), pp. 906-931
- Henrot, A., Oudet, E., Minimizing the second eigenvalue of the Laplace operator with Dirichlet boundary conditions (2003) Arch. Ration. Mech. Anal., 169 (1), pp. 73-87
- Lieb, E.H., Loss, M., (2001) Analysis, , 2nd ed., Grad. Stud. Math. 14, American Mathematical Society, Providence
- Ponce, A.C., A new approach to Sobolev spaces and connections to-convergence (2004) Calc. Var. Partial Differential Equations, 19 (3), pp. 229-255
- Sokoowski, J., Zolésio, J.-P., Introduction to Shape Optimization. Shape Sensitivity Analysis (1992) Springer Ser. Comput. Math., p. 16. , Springer, Berlin
- Šverák, V., On optimal shape design (1993) J. Math. Pures Appl. (9), 72 (6), pp. 537-551
Citas:
---------- APA ----------
Fernández Bonder, J., Rossi, J.D. & Spedaletti, J.F.
(2018)
. Optimal Design Problems for the First p-Fractional Eigenvalue with Mixed Boundary Conditions. Advanced Nonlinear Studies, 18(2), 323-335.
http://dx.doi.org/10.1515/ans-2018-0001---------- CHICAGO ----------
Fernández Bonder, J., Rossi, J.D., Spedaletti, J.F.
"Optimal Design Problems for the First p-Fractional Eigenvalue with Mixed Boundary Conditions"
. Advanced Nonlinear Studies 18, no. 2
(2018) : 323-335.
http://dx.doi.org/10.1515/ans-2018-0001---------- MLA ----------
Fernández Bonder, J., Rossi, J.D., Spedaletti, J.F.
"Optimal Design Problems for the First p-Fractional Eigenvalue with Mixed Boundary Conditions"
. Advanced Nonlinear Studies, vol. 18, no. 2, 2018, pp. 323-335.
http://dx.doi.org/10.1515/ans-2018-0001---------- VANCOUVER ----------
Fernández Bonder, J., Rossi, J.D., Spedaletti, J.F. Optimal Design Problems for the First p-Fractional Eigenvalue with Mixed Boundary Conditions. Adv. Nonlinear Stud. 2018;18(2):323-335.
http://dx.doi.org/10.1515/ans-2018-0001