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Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions

Christian Meyer (2007)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffuse-gray conductive-radiative heat transfer. After stating first-order necessary conditions, second-order sufficient conditions are derived that account for strongly active sets. These conditions ensure local optimality in an Ls-neighborhood of a reference function whereby the underlying analysis allows...

Semilinear elliptic problems with nonlinearities depending on the derivative

David Arcoya, Naira del Toro (2003)

Commentationes Mathematicae Universitatis Carolinae

We deal with the boundary value problem - Δ u ( x ) = λ 1 u ( x ) + g ( u ( x ) ) + h ( x ) , x Ω u ( x ) = 0 , x Ω where Ω N is an smooth bounded domain, λ 1 is the first eigenvalue of the Laplace operator with homogeneous Dirichlet boundary conditions on Ω , h L max { 2 , N / 2 } ( Ω ) and g : N is bounded and continuous. Bifurcation theory is used as the right framework to show the existence of solution provided that g satisfies certain conditions on the origin and at infinity.

Semiregular finite elements in solving some nonlinear problems

Jana Zlámalová (2001)

Applications of Mathematics

In this paper, under the maximum angle condition, the finite element method is analyzed for nonlinear elliptic variational problem formulated in [4]. In [4] the analysis was done under the minimum angle condition.

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