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An existence result for a nonconvex variational problem via regularity

Irene Fonseca, Nicola Fusco, Paolo Marcellini (2002)

ESAIM: Control, Optimisation and Calculus of Variations

Local Lipschitz continuity of minimizers of certain integrals of the Calculus of Variations is obtained when the integrands are convex with respect to the gradient variable, but are not necessarily uniformly convex. In turn, these regularity results entail existence of minimizers of variational problems with non-homogeneous integrands nonconvex with respect to the gradient variable. The x -dependence, explicitly appearing in the integrands, adds significant technical difficulties in the proof.

An existence result for a nonconvex variational problem via regularity

Irene Fonseca, Nicola Fusco, Paolo Marcellini (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Local Lipschitz continuity of minimizers of certain integrals of the Calculus of Variations is obtained when the integrands are convex with respect to the gradient variable, but are not necessarily uniformly convex. In turn, these regularity results entail existence of minimizers of variational problems with non-homogeneous integrands nonconvex with respect to the gradient variable. The x-dependence, explicitly appearing in the integrands, adds significant technical difficulties in the proof.

An existence result for an interior electromagnetic casting problem

Mohammed Barkatou, Diaraf Seck, Idrissa Ly (2006)

Open Mathematics

This paper deals with an interior electromagnetic casting (free boundary) problem. We begin by showing that the associated shape optimization problem has a solution which is of class C 2. Then, using the shape derivative and the maximum principle, we give a sufficient condition that the minimum obtained solves our problem.

An existence result for nonlinear evolution equations of second order

Dimitrios A. Kandilakis (1996)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider a second order differential equation involving the difference of two monotone operators. Using an auxiliary equation, a priori bounds and a compactness argument we show that the differential equation has a local solution. An example is also presented in detail.

An existence theorem for an hyperbolic differential inclusion in Banach spaces

Mouffak Benchohra, Sotiris K. Ntouyas (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we investigate the existence of solutions on unbounded domain to a hyperbolic differential inclusion in Banach spaces. We shall rely on a fixed point theorem due to Ma which is an extension to multivalued between locally convex topological spaces of Schaefer's theorem.

An existence theorem for the Yamabe problem on manifolds with boundary

Simon Brendle, Szu-Yu Sophie Chen (2014)

Journal of the European Mathematical Society

Let ( M , g ) be a compact Riemannian manifold with boundary. We consider the problem (first studied by Escobar in 1992) of finding a conformal metric with constant scalar curvature in the interior and zero mean curvature on the boundary. Using a local test function construction, we are able to settle most cases left open by Escobar’s work. Moreover, we reduce the remaining cases to the positive mass theorem.

An instantaneous semi-Lagrangian approach for boundary control of a melting problem

Youness Mezzan, Moulay Hicham Tber (2021)

Applications of Mathematics

In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on the characteristics method. The resulting time independent control problems are formulated as function space optimization problems with complementarity constraints. At each time step, the existence of an optimal solution is proved and first-order optimality conditions...

Currently displaying 181 – 200 of 287