Alternating Iteration and Elliptic Variational Inequalities.
A-monotone nonlinear relaxed cocoercive variational inclusions
Based on the notion of A - monotonicity, a new class of nonlinear variational inclusion problems is presented. Since A - monotonicity generalizes H - monotonicity (and in turn, generalizes maximal monotonicity), results thus obtained, are general in nature.
An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator...
An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator...
An abstract differential inequality and eigenvalues of variational inequalities
An abstract setting for differential Riccati equations in optimal control problems for hyperbolic/Petrowski-type P. D. E. s with boundary control and slightly smoothing observation.
An active set strategy based on the augmented lagrangian formulation for image restoration
An active set strategy based on the augmented Lagrangian formulation for image restoration
Lagrangian and augmented Lagrangian methods for nondifferentiable optimization problems that arise from the total bounded variation formulation of image restoration problems are analyzed. Conditional convergence of the Uzawa algorithm and unconditional convergence of the first order augmented Lagrangian schemes are discussed. A Newton type method based on an active set strategy defined by means of the dual variables is developed and analyzed. Numerical examples for blocky signals and images perturbed by...
An alternative functional approach to exact controllability of reversible systems.
An analysis of a contact problem for a cylindrical shell: A primary and dual formulation
In this paper the contact problem for a cylindrical shell and a stiff punch is studied. The existence and uniqueness of a solution is verified. The finite element method is discussed.
An application of conjugate duality for numerical solution of continuous convex optimal control problems
An approximation of solutions of variational inequalities.
An approximation scheme for the optimal control of diffusion processes
An approximation theorem for sequences of linear strains and its applications
We establish an approximation theorem for a sequence of linear elastic strains approaching a compact set in by the sequence of linear strains of mapping bounded in Sobolev space . We apply this result to establish equalities for semiconvex envelopes for functions defined on linear strains via a construction of quasiconvex functions with linear growth.
An approximation theorem for sequences of linear strains and its applications
We establish an approximation theorem for a sequence of linear elastic strains approaching a compact set in L1 by the sequence of linear strains of mapping bounded in Sobolev space W1,p . We apply this result to establish equalities for semiconvex envelopes for functions defined on linear strains via a construction of quasiconvex functions with linear growth.
An asymptotical variational principle associated with the steepest descent method for a convex function.
An elementary proof of Marcellini Sbordone semicontinuity theorem
The weak lower semicontinuity of the functional is a classical topic that was studied thoroughly. It was shown that if the function is continuous and convex in the last variable, the functional is sequentially weakly lower semicontinuous on . However, the known proofs use advanced instruments of real and functional analysis. Our aim here is to present a proof understandable even for students familiar only with the elementary measure theory.
An Elliptic Neumann Problem with Subcritical Nonlinearity
We establish the existence of a solution to the Neumann problem in the half-space with a subcritical nonlinearity on the boundary. Solutions are obtained through the constrained minimization or minimax. The existence of solutions depends on the shape of a boundary coefficient.
An evolutionary double-well problem
An example in the gradient theory of phase transitions
We prove by giving an example that when the asymptotic behavior of functionals is quite different with respect to the planar case. In particular we show that the one-dimensional ansatz due to Aviles and Giga in the planar case (see [2]) is no longer true in higher dimensions.