1,721,174 research outputs found
Shape Optimization Problems over Classes of Convex Domains
No full textWe consider shape optimization problems of the form min I {∫∂A f(x, ν(x)) dHn-1 : A ∈ A} where f is any continuous function and the class A of admissible domains is made of convex sets. We prove the existence of an optimal solution provided the domains satisfy some suitable constraints
A shape optimal control problem with changing sign data
No full textIn this paper we consider a shape optimization problem in which the data in the cost functional and in the state equation may change sign, and so no monotonicity assumption is satisfied. Nevertheless, we are able to prove that an optimal domain exists. We also deduce some necessary conditions of optimality for the optimal domain. The results are applied to show the existence of an optimal domain in the case where the cost functional is completely identified, while the right-hand side in the state equation is only known up to a probability P in the space L2(D)
Lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands
No full text
Some Inequalities Involving Perimeter and Torsional Rigidity
No full textWe consider shape functionals of the form Fq(Ω) = P(Ω) Tq(Ω) on the class of open sets of prescribed Lebesgue measure. Here q> 0 is fixed, P(Ω) denotes the perimeter of Ω and T(Ω) is the torsional rigidity of Ω. The minimization and maximization of Fq(Ω) is considered on various classes of admissible domains Ω : in the class Aall of all domains, in the class Aconvex of convex domains, and in the class Athin of thin domains
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