Abstract:
In this paper we study two optimal design problems associated to fractional Sobolev spaces Ws,p(Ω). Then we find a relationship between these two problems and finally we investigate the convergence when s↑1. © 2017 Elsevier Inc.
Registro:
Documento: |
Artículo
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Título: | Some nonlocal optimal design problems |
Autor: | Fernández Bonder, J.; Spedaletti, J.F. |
Filiación: | Departamento de Matemática, FCEN, Universidad de Buenos Aires, IMAS – CONICET, Ciudad Universitaria, Pabellón I, Av. Cantilo 2160, Buenos Aires, C1428EGA, Argentina Departamento de Matemática, Universidad Nacional de San Luis, IMASL – CONICET, Ejército de los Andes 950, San Luis, D5700HHW, Argentina
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Palabras clave: | Fractional laplacian; Gamma convergence; Shape optimization |
Año: | 2018
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Volumen: | 459
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Número: | 2
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Página de inicio: | 906
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Página de fin: | 931
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DOI: |
http://dx.doi.org/10.1016/j.jmaa.2017.11.015 |
Título revista: | Journal of Mathematical Analysis and Applications
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Título revista abreviado: | J. Math. Anal. Appl.
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ISSN: | 0022247X
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v459_n2_p906_FernandezBonder |
Referencias:
- Adams, R.A., Sobolev Spaces (1975) Pure and Applied Mathematics, 65. , Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers] New York–London
- Bourgain, J., Brezis, H., Mironescu, P., Another look at Sobolev spaces (2001) Optimal Control and Partial Differential Equations, , Original research article appeared IOS Press
- Braides, A., Γ-Convergence for Beginners (2002) Oxford Lecture Series in Mathematics and Its Applications, 22. , Oxford University Press Oxford
- Brasco, L., Franzina, G., Convexity properties of Dirichlet integrals and Picone-type inequalities (2014) Kodai Math. J., 37 (3), pp. 769-799
- Dal Maso, G., An Introduction to Γ-Convergence (1993) Progress in Nonlinear Differential Equations and Their Applications, 8. , Birkhäuser Boston, Inc. Boston, MA
- Del Pezzo, L., Fernández Bonder, J., López-Ríos, L., An optimization problem for the first eigenvalue of the p-fractional laplacian (2016) Math. Nachr., , in press
- Di Castro, A., Kuusi, T., Palatucci, G., Local behavior of fractional p-minimizers (2016) Ann. Inst. H. Poincaré Anal. Non Linéaire, 33 (5), pp. 1279-1299
- 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., Giubergia, G.O., Mazzone, F.D., An optimization problem for nonlinear Steklov eigenvalues with a boundary potential (2014) J. Math. Anal. Appl., 417 (1), pp. 234-243
- Fernández Bonder, J., Groisman, P., Rossi, J.D., Optimization of the first Steklov eigenvalue in domains with holes: a shape derivative approach (2007) Ann. Mat. Pura Appl. (4), 186 (2), pp. 341-358
- Fernández Bonder, J., Rossi, J.D., Wolanski, N., Regularity of the free boundary in an optimization problem related to the best Sobolev trace constant (2005) SIAM J. Control Optim., 44 (5), pp. 1614-1635
- Fernández Bonder, J., Rossi, J.D., Wolanski, N., On the best Sobolev trace constant and extremals in domains with holes (2006) Bull. Sci. Math., 130 (7), pp. 565-579
- Laskin, N., Fractional Schrödinger equation (2002) Phys. Rev. E (3), 66 (5). , 7 pp
- Lieb, E.H., Loss, M., Analysis (2001) Graduate Studies in Mathematics, 14. , second edition American Mathematical Society Providence, RI
- Maz'ya, V., Sobolev Spaces with Applications to Elliptic Partial Differential Equations (2011) Grundlehren der Mathematischen Wissenschaften, 342. , augmented edition Fundamental Principles of Mathematical Sciences Springer Heidelberg
- Ponce, A.C., A new approach to Sobolev spaces and connections to Γ-convergence (2004) Calc. Var. Partial Differential Equations, 19 (3), pp. 229-255
Citas:
---------- APA ----------
Fernández Bonder, J. & Spedaletti, J.F.
(2018)
. Some nonlocal optimal design problems. Journal of Mathematical Analysis and Applications, 459(2), 906-931.
http://dx.doi.org/10.1016/j.jmaa.2017.11.015---------- CHICAGO ----------
Fernández Bonder, J., Spedaletti, J.F.
"Some nonlocal optimal design problems"
. Journal of Mathematical Analysis and Applications 459, no. 2
(2018) : 906-931.
http://dx.doi.org/10.1016/j.jmaa.2017.11.015---------- MLA ----------
Fernández Bonder, J., Spedaletti, J.F.
"Some nonlocal optimal design problems"
. Journal of Mathematical Analysis and Applications, vol. 459, no. 2, 2018, pp. 906-931.
http://dx.doi.org/10.1016/j.jmaa.2017.11.015---------- VANCOUVER ----------
Fernández Bonder, J., Spedaletti, J.F. Some nonlocal optimal design problems. J. Math. Anal. Appl. 2018;459(2):906-931.
http://dx.doi.org/10.1016/j.jmaa.2017.11.015