Constructive Sobolev gradient preconditioning for semilinear elliptic systems.
Contact between elastic bodies. I. Continuous problems
Problems of a unilateral contact between bounded bodies without friction are considered within the range of two-dimensional linear elastostatics. Two classes of problems are distinguished: those with a bounded contact zone and with an enlargign contact zone. Both classes can be formulated in terms of displacements by means of a variational inequality. The proofs of existence of a solution are presented and the uniqueness discussed.
Contact between elastic bodies. II. Finite element analysis
The paper deals with the approximation of contact problems of two elastic bodies by finite element method. Using piecewise linear finite elements, some error estimates are derived, assuming that the exact solution is sufficiently smooth. If the solution is not regular, the convergence itself is proven. This analysis is given for two types of contact problems: with a bounded contact zone and with enlarging contact zone.
Contact between elastic bodies. III. Dual finite element analysis
The problem of a unilateral contact between elastic bodies with an apriori bounded contact zone is formulated in terms of stresses via the principle of complementary energy. Approximations are defined by means of self-equilibriated triangular block-elements and an -error estimate is proven provided the exact solution is regular enough.
Contact between elastic perfectly plastic bodies
If the material of the bodies is elastic perfectly plastic, obeying the Hencky's law, the formulation in terms of stresses is more suitable than that in displacements. The Haar-Kármán principle is first extended to the case of a unilateral contact between two bodies without friction. Approximations are proposed by means of piecewise constant triangular finite elements. Convergence of the method is proved for any regular family of triangulations.
Contact problems with bounded friction. Coercive case
Contact problems with bounded friction. Semicoercive case
Contact problems with given time-dependent friction force in linear viscoelasticity
Contact shape optimization based on the reciprocal variational formulation
The paper deals with a class of optimal shape design problems for elastic bodies unilaterally supported by a rigid foundation. Cost and constraint functionals defining the problem depend on contact stresses, i.e. their control is of primal interest. To this end, the so-called reciprocal variational formulation of contact problems making it possible to approximate directly the contact stresses is used. The existence and approximation results are established. The sensitivity analysis is carried out....
Contents
Continuity, curvature, and the general covariance of optimal transportation
Continuity of Minimal Surfaces with Piecewise Smooth Free Boundaries.
Continuity of solutions to a basic problem in the calculus of variations
We study the problem of minimizing over the functions that assume given boundary values on . The lagrangian and the domain are assumed convex. A new type of hypothesis on the boundary function is introduced: thelower (or upper) bounded slope condition. This condition, which is less restrictive than the familiar bounded slope condition of Hartman, Nirenberg and Stampacchia, allows us to extend the classical Hilbert-Haar regularity theory to the case of semiconvex (or semiconcave) boundary...
Continuity of the non-convex play operator in the space of rectifiable curves
We prove that the vector play operator with a uniformly prox-regular characteristic set of constraints is continuous with respect to the -norm and to the -strict metric in the space of rectifiable curves, i.e., in the space of continuous functions of bounded variation. We do not assume any further regularity of the characteristic set. We also prove that the non-convex play operator is rate independent.
Continuity properties of projection operators.
Continuous adjoint approach to shape optimization with respect to 2D incompressible fluid flow
The aim of this article is to briefly introduce the procedure for optimizing water turbine blades, which can lead to an innovative blade design and, consequently, an improvement in the desired properties of the water turbine, such as efficiency or the preferred pressure distribution on the blade. The computational method is based on formulating an objective function under certain constraint conditions, which are governed by the Navier-Stokes equations. This formulation enables the use of the Lagrange...
Continuous dependence estimates for the ergodic problem of Bellman-Isaacs operators via the parabolic Cauchy problem
This paper concerns continuous dependence estimates for Hamilton-Jacobi-Bellman-Isaacs operators. We establish such an estimate for the parabolic Cauchy problem in the whole space [0, +∞) × ℝn and, under some periodicity and either ellipticity or controllability assumptions, we deduce a similar estimate for the ergodic constant associated to the operator. An interesting byproduct of the latter result will be the local uniform convergence for some classes of singular perturbation problems.
Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations.
Continuous dependence on function parameters for superlinear Dirichlet problems
We discuss the existence of solutions for a certain generalization of the membrane equation and their continuous dependence on function parameters. We apply variational methods and consider the PDE as the Euler-Lagrange equation for a certain integral functional, which is not necessarily convex and coercive. As a consequence of the duality theory we obtain variational principles for our problem and some numerical results concerning approximation of solutions.
Continuous dependence on obstacles in double global obstacle problems.