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Abstract:

We consider the optimization problem of minimizing ∫Ω | ∇ u |p d x with a constraint on the volume of { u > 0 }. We consider a penalization problem, and we prove that for small values of the penalization parameter, the constrained volume is attained. In this way we prove that every solution u is locally Lipschitz continuous and that the free boundary, ∂ { u > 0 } ∩ Ω, is smooth. © 2006 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:An optimization problem with volume constraint for a degenerate quasilinear operator
Autor:Fernández Bonder, J.; Martínez, S.; Wolanski, N.
Filiación:Departamento de Matemática, FCEyN, UBA, 1428 Buenos Aires, Argentina
Palabras clave:Free boundaries; Optimal design problems
Año:2006
Volumen:227
Número:1
Página de inicio:80
Página de fin:101
DOI: http://dx.doi.org/10.1016/j.jde.2006.03.006
Título revista:Journal of Differential Equations
Título revista abreviado:J. Differ. Equ.
ISSN:00220396
CODEN:JDEQA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00220396_v227_n1_p80_FernandezBonder.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v227_n1_p80_FernandezBonder

Referencias:

  • Acker, A., An extremal problem involving distributed resistance (1981) SIAM J. Math. Anal., 12, pp. 169-172
  • Aguilera, N., Alt, H.W., Caffarelli, L.A., An optimization problem with volume constraint (1986) SIAM J. Control Optim., 24 (2), pp. 191-198
  • Aguilera, N., Caffarelli, L.A., Spruck, J., An optimization problem in heat conduction (1988) Ann. Sc. Norm. Super. Pisa Cl. Sci. (4), 14 (3), pp. 355-387
  • Alt, H.W., Caffarelli, L.A., Existence and regularity for a minimum problem with free boundary (1981) J. Reine Angew. Math., 325, pp. 105-144
  • Danielli, D., Petrosyan, A., A minimum problem with free boundary for a degenerate quasilinear operator (2005) Calc. Var. Partial Differential Equations, 23 (1), pp. 97-124
  • Danielli, D., Petrosyan, A., Shahgholian, H., A singular perturbation problem for the p-Laplace operator (2003) Indiana Univ. Math. J., 52 (2), pp. 457-476
  • Federer, H., (1969) Geometric Measure Theory, , Springer, Berlin
  • 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. 1612-1635
  • Flucher, M., An asymptotic formula for the minimal capacity among sets of equal area (1993) Calc. Var. Partial Differential Equations, 1, pp. 71-86
  • Juutinen, P., Lindqvist, P., Manfredi, J.J., On the equivalence of viscosity solutions and weak solutions for a quasi-linear equation (2001) SIAM J. Math. Anal., 33 (3), pp. 699-717
  • Kawohl, B., Rearrangements and Convexity of Level Sets in PDE (1985) Lecture Notes in Math., 1150. , Springer, New York
  • Lederman, C., A free boundary problem with a volume penalization (1996) Ann. Sc. Norm. Super. Pisa Cl. Sci., 23 (2), pp. 249-300
  • Teixeira, E., The nonlinear optimization problem in heat conduction (2005) Calc. Var. Partial Differential Equations, 24 (1), pp. 21-46
  • Trudinger, N.S., On Harnack type inequalities and their application to quasilinear elliptic equations (1967) Comm. Pure Appl. Math., 20, pp. 721-747

Citas:

---------- APA ----------
Fernández Bonder, J., Martínez, S. & Wolanski, N. (2006) . An optimization problem with volume constraint for a degenerate quasilinear operator. Journal of Differential Equations, 227(1), 80-101.
http://dx.doi.org/10.1016/j.jde.2006.03.006
---------- CHICAGO ----------
Fernández Bonder, J., Martínez, S., Wolanski, N. "An optimization problem with volume constraint for a degenerate quasilinear operator" . Journal of Differential Equations 227, no. 1 (2006) : 80-101.
http://dx.doi.org/10.1016/j.jde.2006.03.006
---------- MLA ----------
Fernández Bonder, J., Martínez, S., Wolanski, N. "An optimization problem with volume constraint for a degenerate quasilinear operator" . Journal of Differential Equations, vol. 227, no. 1, 2006, pp. 80-101.
http://dx.doi.org/10.1016/j.jde.2006.03.006
---------- VANCOUVER ----------
Fernández Bonder, J., Martínez, S., Wolanski, N. An optimization problem with volume constraint for a degenerate quasilinear operator. J. Differ. Equ. 2006;227(1):80-101.
http://dx.doi.org/10.1016/j.jde.2006.03.006