Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 1, pp. 143155 (1999) 

Global Solution of Optimal Shape Design ProblemsA. Fakharzadeh J. and J. E. RubioA. Fakharzadeh J.: Shahid Chamran University of Ahwaz, Dept. Math., Ahwaz, Iran; email: science@www.dci.co.irJ. E. Rubio: University of Leeds, Dept. Appl. Math. Studies, Leeds, LS2 9JT, UK Abstract: We consider optimal shape design problems defined by pairs of geometrical elements and control functions associated with linear or nonlinear elliptic equations. First, necessary conditions are illustrated in a variational form. Then by applying an embedding process, the problem is extended into a measuretheoretical one, which has some advantages. The theory suggests the development of a computational method consisting of the solution of a finitedimensional linear programming problem. Nearly optimal shapes and related controls can thus be constructed. Two examples are also given. Keywords: embedding methods, optimal shape design, Radon measures, linear programming, optimal shape, optimal control, elliptic equations Classification (MSC2000): 49XX Full text of the article:
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