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2008 | Vol. 37, no 4 | 811-829
Tytuł artykułu

The eigenvalue problem with conductivity boundary conditions

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we study isoperimetric inequalities for the eigenvalues of the Laplace operator with constant and locally constant boundary conditions. Existence and stability results are presented in the of the gamma and weak gamma convergencies, together with identification of optimal sets by analytical and numerical methods.
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811-829
Opis fizyczny
Bibliogr. 15 poz., rys.
Twórcy
autor
autor
autor
  • Laboratoire de Mathematiques, CNRS UMR 5127 Universite de Savoie Campus Scientifique, 73376 Le-Bourget-Du-Lac, Prance, dorin.bucur@univ-savoie.fr
Bibliografia
  • ALESSANDRINI, G. and DIAZ VALENZUELA, A. (1996) Unique determination of multiple cracks by two measurements. SI AM J. Control Optim. 34 (3), 913-921.
  • BELHACHMI, Z. and BUCUR, D. (2007) Stability and uniqueness for crack identification problem. SIAM J. Control Optim. 46 (1), 253-273.
  • BUCUR, D. and BUTTAZZO, G. 2005 Variational Methods in Shape Optimization Problems. Progress in Nonlinear Differential Equations and Their Applications 65, Birkhäuser, Basel, Boston.
  • BUCUR, D. and VARCHON, N. (2002) A duality approach for the boundary variation of Neumann problems. SIAM J. Math. Anal. 34 (2), 460-477.
  • BUTTAZZO, G. and DAL MASO, G. (1993) An existence result for a class of shape Optimization Problems. Arch. Rational Mech. Anal. 122 (2), 183-195.
  • DELFOUR, M. C. and ZOLESIO, J.P. (2001) Shapes and Geometries. Analysis, differential calculus, and optimization. Advances in Design and Control 4. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
  • DUNFORD, N. and SCHWARTZ, J.T. (1963). Linear Operators. Part II: Spectral Theory. Interscience Publishers, New York, London,
  • FREITAS, P. and HENROT, A. (2004) On the first twisted Dirichlet eigenvalue. Commun. Anal. Geom. 12, 1083-1103.
  • FRIEDMAN, A. and VOGELIUS, M. (1989) Determining cracks by boundary measurements. Indiana Univ. Math. J. 38 (3), 527-556.
  • GRECO, A. and LUCIA, M. (2008) Laplacian eigenvalues for mean zero functions with constant Dirichlet data. Forum Math, (to appear).
  • HENROT, A. (2006) Extremum Pproblems for Eigenvalues of Elliptic Operators. Frontiers in Mathematics, Birkhäuser Verlag, Basel.
  • KAWOHL, B. (1985) Rearrangements and Convexity of Level Sets in PDE. Lecture Notes in Mathematics 1150. Springer-Verlag, Berlin.
  • PARDALOS, P.M. and ROMEIJN, H.E., EDS. (2002) Handbook of Global Optimization. Vol. 2. Nonconvex Optimization and its Applications 62, Kluwer Academic Publishers, Dordrecht.
  • SHEWCHUK, J.R. (1996) Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator. In: Ming C. Lin and Dinesh Manocha, eds., Applied Computational Geometry: Towards Geometric Engineering of Lecture Notes in Computer Science 1148, Springer-Verlag, Berlin, 203-222.
  • SOKOŁOWSKI, J. and ZOLÉSIO, J.P. (1992) Introduction to Shape Optimization. Shape sensitivity analysis. Springer Series in Computational Mathematics 16, Springer-Verlag, Berlin.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0034-0004
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