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Shape differentiability of the Neumann problem of the Laplace equation in the half-space

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We deal with the existence of the material derivative of the Laplace equation with the Neumann boundary condition in the half space. We consider two different perturbations of domains to get the existence of weak Gateaux material derivative and the existence of Fréchet material derivatives.
Rocznik
Strony
747--769
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
autor
  • Universite de Pau et des Pays de L'Adour, Laboratoire de Mathematiques Appliquees I.P.R.A and CNRS UMR 5142, Av. de l'Universite, 64000 Pau, France
Bibliografia
  • AMROUCHE, C., GIRAULT, V., GIROIRE, J. (1994) Weighted Sobolev spaces for Laplace’s equation in RN. J. Math. Pures Appl. 73, 579-606.
  • AMROUCHE, C. (2002) The Neumann problem in the half- space. C. R. Acad. Sci. Paris, Ser. I 335, 151-156.
  • AMROUCHE, C., NECASOVA, S. and SOKOLOWSKI, J. (2004) Shape sensitivity analysis of the Dirichlet Laplacian in the Half- space. Bull. Pol. Acad. Sciences Math. 52 (4), 365-380.
  • AMROUCHE, C. and NECASOVA, S. (2001) Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition. Mathematica Bohemica 126 (2), 265-274.
  • BOULMEZAOUD, T.Z. (1999) Espaces de Sobolev avec poids pour 1’equation de Laplace dans le demi-espace. C. R. Acad. Sci. Paris Ser. I, 328, 221-226.
  • BOULMEZAOUD, T.Z. (2001) On the Stokes problem and on the biharmonic equation in the half - space: an approach via weighted Sobolev spaces. Math. Methods in the Applied Sciences 25, 373-398.
  • DELFOUR, M. and ZOLESIO, J.P. (2001) Shapes and Geometries: Analysis, Differential Calculus, and Optimisation. SIAM series on Advances in Design and Control, Philadelphia.
  • GIRAULT, V. (1992) The gradient, divergence, curl and Stokes operators in weighted Sobolev spaces of R3. J. Fac. Sci. Univ. Tokyo, Sect. I A, Math. 39, 279-307.
  • GIROIRE, J. (1987) Etude de quelques problemes aux Limites Exterieurs et Resolution par Equation Integrales. These de Doctorat, Univ. Pierre et Marie Curie.
  • FREMIOT, G. (2000) Structure de la semi-derivee eulerienne dans le cas de domaines fissurés et quelques applications. PhD Thesis of University Henri Poincare Nancy, 1.
  • HANOUZET, B. (1971) Espaces de Sobolev avec poids. Application au probleme de Dirichlet dans un demi-espace. Rend. Sem. Univ. Padova 46, 227-272.
  • KUFNER, A. (1985) Weighted Sobolev Spaces. Wiley, Chichester.
  • KUFNER, A. and OPIC, B. (1990) Hardy-type Inequalities, Wiley, New York.
  • KUDRYAVTSEV, L.D. (1959) Direct and inverse imbedding theorems. Application to the solution of elliptic equations by variational method. Trudy Mat. Inst. Steklov 55, 1-182.
  • LAURIN, A. (2006) Domaines singulierement perturbes en optimisation de formes. PhD Thesis of University Henri Poincare Nancy 1.
  • LIZORKIN, P.I. (1981) The behavior at infinity of functions in Liouville class. On Riesz potentials of arbitrary order. Proc. of the Steklov Inst. of Math. 4, 185-209.
  • LEROUX, M.N. (1974) Resolution numerique du Probleme du Potentiel dans le Plan par une Methode Variationnelle d’Element Fini. These, Univ. de Rennes.
  • MAZ’YA, V.G., PLAMENEVSKII, B.A. and STUPYALIS, L.I. (1984) The three-dimensional problem of steady-state motion of a fluid with a free surface. Amer. Math. Soc. Transl. 123 (2), 171-268.
  • MURAT, F. and SIMON, J. (1976) Sur la Controle par un Domaine Geometrique. Publications du Laboratoire d’Analyse Numerique, Universite de Paris VI.
  • NEČAS, J. (1962) Sur une méthode pour résoudre les équations aux dérivées partielles du type elliptique, voisine de la variationelle. Ann. Scuola Norm. Sup. Pisa 16, 305-326.
  • NIKOL’SKII, S.M. (1977) Approximation of functions of several variables and embedding theorems. Nauka, Moscow, (in Russian).
  • PIRONNEAU, O. (1984) Optimal Shape Design for Elliptic Systems. Springer series in Computational Physics, Springer-Verlag, New York.
  • SOKOLOWSKI, J. and ZOLESIO, J.P. (1992) Introduction to Shape Optimization. Springer - Verlag.
  • SCHUMACHER, K. (2007) The Navier- Stokes equations with low - regularity data in weighted function spaces. PhD. thesis.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0034-0001
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