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We consider a mathematical model of a quasistatic contact between an elastic body and an obstacle. The contact is modelled with unilateral constraint and normal compliance, associated to a version of Coulomb's law of dry friction where the coefficient of friction depends on the slip displacement. We present a weak formulation of the problem and establish an existence result. The proofs employ a time-discretization method, compactness and lower semicontinuity arguments.
In this paper we study a nonlinear evolution inclusion of subdifferential
type in Hilbert spaces. The perturbation term is Hausdorff continuous in
the state variable and has closed but not necessarily convex values. Our result
is a stochastic generalization of an existence theorem proved by Kravvaritis and
Papageorgiou in [6].
We prove a ratio ergodic theorem for non-singular free and actions, along balls in an arbitrary norm. Using a Chacon–Ornstein type lemma the proof is reduced to a statement about
the amount of mass of a probability measure that can concentrate on (thickened) boundaries of balls in . The proof relies on geometric properties of norms, including the Besicovitch covering lemma and the fact that boundaries of balls have lower dimension than the ambient space. We also
show that for general group...
Using monotone bifunctions, we introduce a recession concept
for general equilibrium problems relying on a variational convergence notion. The interesting purpose is to extend some results of P. L. Lions on
variational problems. In the process we generalize some results by H. Brezis
and H. Attouch relative to the convergence of the resolvents associated with
maximal monotone operators.
Shape optimization is described by finding the geometry of a structure which is optimal in the sense of a minimized cost function with respect to certain constraints. A Newton’s mesh independence principle was very efficiently used to solve a certain class of optimal design problems in [6]. Here motivated by optimization considerations we show that under the same computational cost an even finer mesh independence principle can be given.
The question whether a hyponormal weighted shift with trace class self-commutator is the compression modulo the Hilbert-Schmidt class of a normal operator, remains open. It is natural to ask whether Putinar's construction through which he proved that hyponormal operators are subscalar operators provides the answer to the above question. We show that the normal extension provided by Putinar's theory does not lead to the extension that would provide a positive answer to the question.
The uniqueness of the Wold decomposition of a finite-dimensional stationary process without assumption of full rank stationary process and the Lebesgue decomposition of its spectral measure is easily obtained.
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