Subtitle:

Raport Badawczy = Research Report ; RB/94/2003

Publisher:

Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences

Place of publishing:

Warszawa

Description:

503-528 pages ; 21 cm ; Bibliography p. 527-528

Abstract:

The stability issue of critical shapes for shape optimization problems with the state function given by a solution to the Neumann problem for the Laplace equation is considered. To this end, the properties of the shape Hessian evaluated at critical shapes are analysed. First, it is proved that the stability cannot be expected for the model problem. Then, the new estimates for the shape Hessian are derived in order to overcome the classical two norms-discrepancy well know in control problems, Malanowski (2001). In the context of shape optimization, the situation is similar compared to control problems, actually, the shape Hessian can be coercive only in the norm strictly weaker with respect to the norm of the second order ifferentiability of the shape functional. In addition, it is shown that an appropriate regularization makes possible the stability of critical shapes.

Relation:

Raport Badawczy = Research Report

Detailed Resource Type:

Report

Resource Identifier:

oai:rcin.org.pl:217409

Source:

RB-2003-94

Language:

eng

Language of abstract:

eng

Rights:

Creative Commons Attribution BY 4.0 license

Terms of use:

Copyright-protected material. [CC BY 4.0] May be used within the scope specified in Creative Commons Attribution BY 4.0 license, full text available at: ; -

Digitizing institution:

Systems Research Institute of the Polish Academy of Sciences

Original in:

Library of Systems Research Institute PAS

Projects co-financed by:

Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.

Access:

Open