6 papers
A novel way of computing the shape derivative for a class of non-smooth PDEs and its impact on deriving necessary conditions for locally optimal shapes
Livia Betz
We derive necessary conditions for locally optimal shapes of a design problem governed by a non-smooth PDE. The main particularity of the state system is the lack of differentiabil…
Sensitivity analysis of a Signorini-type history-dependent variational inequality
Livia Betz, Andaluzia Matei, Mircea Sofonea
We consider a history-dependent variational inequality (P) which models the frictionless contact between a viscoelastic body and a rigid obstacle covered by a layer of soft materia…
Necessary conditions for the optimal control of a shape optimization problem with non-smooth PDE constraints
Livia Betz
This paper is concerned with the derivation of necessary conditions for the optimal shape of a design problem governed by a non-smooth PDE. The main particularity thereof is the la…
Optimal control of a non-smooth elliptic PDE with non-linear term acting on the control
Livia Betz
This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smo…
Approximation of shape optimization problems with non-smooth PDE constraints
Livia Betz
This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow th…
Optimality conditions for the control of a rate independent system with history variable
Livia Betz
This paper addresses an optimal control problem governed by a rate independent evolution involving an integral operator. Its particular feature is that the dissipation potential de…