PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2005 | 3 | 1 | 39-57
Tytuł artykułu

An existence result for a quadrature surface free boundary problem

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
1
Strony
39-57
Opis fizyczny
Daty
wydano
2005-03-01
online
2005-03-01
Twórcy
autor
Bibliografia
  • [1] H.W. Alt and L.A. Caffarelli: “Existence and regularity for a minimum problem with free boundary”, J. Reine angew. Math., Vol. 325, (1981), pp. 105–144.
  • [2] M. Barkatou, D. Seck and I. Ly: “An existence result for a free boundary problem for the p-Laplace operator”, submitted.
  • [3] M. Barkatou: “Some geometric properties for a class of non Lipschitz-domains”, New York J. of Math., Vol. 8, (2002), pp. 189–213.
  • [4] M. Barkatou: “Existence of quadrature surfaces for a uniform density supported by a segment”, submitted.
  • [5] J.A. Bello, E. Fernandez-Cara, J. Lemoine and J. Simon: “On drag differentiability for Lipschitz domains”, Control of Part. Diff. Eq. and Appl., Lec. Notes In Pure and Applied Math. Series, Vol. 174, (1995), Dekker, New York.
  • [6] A. Beurling: “On free-boundary problems for the Laplace equation”, Sem. Anal. Funct., Inst. Adv. Study Princeton, Vol. 1, (1957), pp. 248–263.
  • [7] D. Bucur and P. Trebeschi: “Shape Optimization Problems Governed by Nonlinear State Equations”, Proc. Roy. Sc. Edinburgh, Vol. 128 A (1998), pp. 945–963.
  • [8] D. Bucur and J.P. Zolesio: “N-dimensional shape optimization under capacitary constraints”, J. Diff. Eq., Vol. 123(2), (1995), pp. 504–522. http://dx.doi.org/10.1006/jdeq.1995.1171
  • [9] G. Buttazzo, V. Ferone and B. Kawhol: “Minimum problems over sets of concave functions and related questions”, Math. Nachr., (1995), pp. 71–89.
  • [10] T. Carleman: “Über ein Minimumproblem der mathematischen Physik”,Math. Z.,Vol. 1, (1918),pp.208–212. http://dx.doi.org/10.1007/BF01203612
  • [11] D. Chenais, “On the existence of a solution in a domain identification problem”, J. Math. Anal. Appl., Vol. 52, (1975), pp. 189–289. http://dx.doi.org/10.1016/0022-247X(75)90091-8
  • [12] R. Dautray and J.L. Lions: Analyse mathématique et calcul numérique pour les sciences et les techniques, Vol. 1, 2, Masson, Paris, 1984
  • [13] E. DiBendetto: “ C 1+∞ local regularity of weak solutions of degenerate elliptic equations”, Nonlinear Analysis., Vol. 7, (1983), pp. 827–850. http://dx.doi.org/10.1016/0362-546X(83)90061-5
  • [14] K. Friedrichs: “Über ein Minimumproblem für Potentialströmungen mit freiem Rand”.Math. Ann.,Vol. 109, (1934),pp.208–212.
  • [15] G. Gidas, Wei-Ming Ni and L. Nirenberg: “Symmetry and related properties via the maximum principle”,Comm. Math. Phys., Vol. 68, (1979),pp.209–300. http://dx.doi.org/10.1007/BF01221125
  • [16] B. Gustafsson and H. Shahgholian: “Existence and geometric properties of solutions of a free boundary problem in potential theory”, J. Reine angew. Math., Vol. 473, (1996), pp. 137–179.
  • [17] A. Henrot: “Subsolutions and supersolutions in a free boundary problem”, Arkiv för Math., Vol. 32(1), (1994), pp. 79–98.
  • [18] H. Hosseinzadeh and H. Shahgholian: “Some qualitative aspects of a free boundary problem for the p-Laplacian”, Ann. Acad. Scient. Fenn. Math., Vol. 24, (1999), pp. 109–121.
  • [19] D. Gilbarg and N.S. Trudinger: Elliptic partial equations of second order, Springer-Verlag, 1983.
  • [20] M.V. Keldyš: “On the solvability and the stability of the Dirichlet problem”, Amer. Math. Soc. Trans., Vol. 51 (2), (1966), pp. 1–73.
  • [21] J.L. Lewis: “Regularity of the derivatives of solutions to certain degenerate elliptic equations”, Indiana Univ. Math. J., Vol. 32, (1983), pp. 849–858. http://dx.doi.org/10.1512/iumj.1983.32.32058
  • [22] G.M. Lieberman: “Boundary regularity for solutions of degenerate elliptic equations”, Nonlinear Analysis., Vol. 12, (1988), pp. 1203–1219. http://dx.doi.org/10.1016/0362-546X(88)90053-3
  • [23] V. Mikhailov: Équation aux dérivées partielles, Mir, Moscow, 1980.
  • [24] F. Murat and J. Simon: “Quelques résultats sur le contrôle par un domaine géométrique”, Publ. du labo. d’Anal. Num., Paris VI, (1974), pp. 1–46.
  • [25] O. Pironneau: Optimal shape design for elliptic systems, Springer series in Computational Physics, Springer, New York, 1984.
  • [26] J. Serrin: “A symmetry problem in potential theory”,Arch. Rat. Mech. Anal.,Vol. 43, (1971),pp.304–318. http://dx.doi.org/10.1007/BF00250468
  • [27] H. Shahgholian: “Quadrature surfaces as free boundaries”, Arkiv för Math., Vol. 32(2), (1994), pp. 475–492.
  • [28] J. Sokolowski and J.P. Zolesio: Introduction to shape optimization: shape sensitity analysis, Springer Series in Computational Mathematics, Vol. 10, Springer, Berlin, 1992.
  • [29] P. Tolksdorf: “On the Dirichlet problem for quasilinear equations in domains with conical boundary points”, Comm. Partial Differential Equations, Vol. 8(7), (1983), pp. 773–817.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475654
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.