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Vector variational problems and applications to optimal design

Pablo Pedregal (2005)

ESAIM: Control, Optimisation and Calculus of Variations

We examine how the use of typical techniques from non-convex vector variational problems can help in understanding optimal design problems in conductivity. After describing the main ideas of the underlying analysis and providing some standard material in an attempt to make the exposition self-contained, we show how those ideas apply to a typical optimal desing problem with two different conducting materials. Then we examine the equivalent relaxed formulation to end up with a new problem whose numerical...

Vector variational problems and applications to optimal design

Pablo Pedregal (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We examine how the use of typical techniques from non-convex vector variational problems can help in understanding optimal design problems in conductivity. After describing the main ideas of the underlying analysis and providing some standard material in an attempt to make the exposition self-contained, we show how those ideas apply to a typical optimal desing problem with two different conducting materials. Then we examine the equivalent relaxed formulation to end up with a new problem whose numerical...

Von Kármán equations. III. Solvability of the von Kármán equations with conditions for geometry of the boundary of the domain

Július Cibula (1991)

Applications of Mathematics

Solvability of the general boundary value problem for von Kármán system of nonlinear equations is studied. The problem is reduced to an operator equation. It is shown that the corresponding functional of energy is coercive and weakly lower semicontinuous. Then the functional of energy attains absolute minimum which is a variational solution of the problem.

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