Shape sensitivity analysis of the Dirichlet Laplacian in a half-space

• Autorzy: Amrouche Ch. , Nečasová S. , Sokołowski J.
• Języki publikacji: EN

Abstrakty

EN

Material and shape derivatives for solutions to the Dirichlet Laplacian in a half-space are derived by an application of the speed method. The proposed method is general and can be used for shape sensitivity analysis in unbounded domains for the Neumann Laplacian as well as for the elasticity boundary value problems.

Słowa kluczowe

EN

shape derivative; material derivative; speed method; Dirichlet Laplacian

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 4
• Strony: 365--380
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Amrouche Ch.

• Laboratoire de Mathématiques Appliquées, I.P.R.A., Université de Pau et des Pays de L’Adour, Av. de l’Université, 64000 Pau, France

autor

Nečasová S.

• Mathematical Institute of the Academy of Sciences, Žitná 25, 11567 Praha 1, Czech Republic

autor

Sokołowski J.

• Institut Elie Cartan, Laboratoire de Mathématiques, Université Henri Poincaré Nancy I, B. P. 239, 54506 Vandœuvre-lès-Nancy Cedex, France

Bibliografia

• [1] C. Amrouche, V. Girault and J. Giroire, Weighted Sobolev spaces for Laplace’s equation in RN, J. Math. Pures Appl. 73, (1994), 579-606.
• [2] C. Amrouche and Š. Nečasová Laplace equation in the half-space with a nonhomogeneous Dirichlet Bondary condition, Math.Bohemica 126 (2001), 265-274.
• [3] T. Z. Boulmezaoud, Epaces de Sobolev avec poids l’equation de Laplace dans le demi-espace, C. R. Acad. Sci. Paris Sér. I 328 (1999), 221-226.
• [4] M. Delfour and J.-P. Zolésio, Shapes and Geometries: Analysis, Differential Calculus, and Optimisation, Advances in Design and Control, SIAM, Philadelphia, 2001.
• [5] B. Hanouzet, Espaces de Sobolev avec poids. Applications au problème de Dirichlet dans un demi-espace, Rend. Sem. Univ. Padova 46 (1971), 227-272.
• [6] V. G. Maz’ya, B. A. Plamenevskiĭ and L. I. Stupyalis, The tyree-dimensional problem of steady-state motion of a fluid with a free surface, in: Amer. Math. Soc. Transl. (2) 123 (1984), 171-268.
• [7] V. G. Maz’ya and T. O. Shaposhnikova, Multipliers in Spaces of Differentiables Functions, Leningrad Univ., Leningrad, 1986 (in Russian).
• [8] J. Sokołowski and J.-P. Zolésio, Introduction to Shape Optimization, Springer, 1992.