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Items for "maximum principle"

Separating positivity and regularity for fourth order Dirichlet problems in 2d-domains

The main result in this paper is that the solution operator for the bi-Laplace problem with zero Dirichlet boundary conditions on a bounded smooth 2d-domain can be split in a positive part and a possibly negative part which both satisfy the zero boundary condition...

Keywords: biharmonic operator, Dirichlet boundary conditions, Green function estimates, positivity, maximum principle

03/2005 | Analysis, Oldenbourg Wissenschaftsverlag

Maximum principles for energy stationary hypersurfaces

We consider critical immersions of singular variational integrals of the type E_α(X) = ∫_M X_{n + 1}^α dA, α > 0...

Keywords: maximum principle, singular variational problem, enclosure theorem, critical immersion, curvature flow

02/2006 | Analysis, Oldenbourg Wissenschaftsverlag

The stochastic maximum principle in optimal control of singular diffusions with non linear coefficients

We consider a stochastic control problem of a non linear system in which the variable control has two components, the first being absolutely continuous and the second singular...

Keywords: maximum principle, singular control, Adjoint equation, variational equation

01/2005 | Random Operators and Stochastic Equations, Walter de Gruyter

Necessary and sufficient conditions of optimality for optimal control problem with initial and terminal costs

We consider a stochastic control problem where the control domain need not be convex, the system is governed by a non linear forward-backward stochastic differential equation with nonconstant terminal condition.The criteria to be minimized is in the general form, with initial and terminal costs. We derive necessary as well as sufficient conditions of optimality by introducing three adjoint equations. This problem may have applications in the financial market and it can be adapted to the problem of the minimization of an initial investment and the maximization of a final wealth.

Keywords: Forward-backward stochastic differential equation, optimal control, maximum principle, Adjoint equation, variational equation