caa a22 4500 388108746 CHVBK 20180307125347.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500019363 doi S0308210500019363 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500019363 Novruzi A. Université Henri Poincaré Nancy 1, Laboratoire de Mathématiques, BP 239, 54506 Vandœuvre-lès-Nancy Cedex, France (novruzi@Oiecn.u-nancy.fr) Cα estimation on the boundary for the gradient of the shape derivative of a Neumann problem in ℝ3 [Elektronische Daten] [A. Novruzi] In this paper we establish a non-global Cα estimation on the boundary for the gradient of the solution of a Neumann exterior problem in ℝ3. The boundary data of this problem are with small compact support and with C0 norm tending to infinity when the diameter of support data goes to zero. This problem appears, for instance, in the numerical shape optimization problems when the Newton method is used. It turns out that the gradient decreases when the distance to the boundary data supports increases (Saint Venant's principle), which, when used in applications, leads to a strong reduction of the gradient computational cost. Copyright © Royal Society of Edinburgh 1999 Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/6(1999), 1229-1250 0308-2105 129:6<1229 1999 129 PRM https://doi.org/10.1017/S0308210500019363 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500019363 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Novruzi A. Université Henri Poincaré Nancy 1, Laboratoire de Mathématiques, BP 239, 54506 Vandœuvre-lès-Nancy Cedex, France (novruzi@Oiecn.u-nancy.fr) NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/6(1999), 1229-1250 0308-2105 129:6<1229 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge