452 research outputs found
An isoperimetric inequality for diffused surfaces
For general varifolds in Euclidean space, we prove an isoperimetric
inequality, adapt the basic theory of generalised weakly differentiable
functions, and obtain several Sobolev type inequalities. We thereby intend to
facilitate the use of varifold theory in the study of diffused surfaces.Comment: Awaiting publication in Kodai Math. J. The final printed version will
be different. 14 pages, no figure
On two inequalities of \v{C}eby\v{s}ev
In this work, several sharp bounds for the \v{C}eby\v{s}ev functional
involving various type of functions are proved. In particular, for the
\v{C}eby\v{s}ev functional of two absolutely continuous functions whose first
derivatives are both convex, convex and belong to -spaces, convex and
bounded variation, convex and Lipschitz mappings new sharp bounds are
presented. Other related results regarding two convex and concave functions are
given.Comment: 11 page
Discrete Approximations of a Controlled Sweeping Process
The paper is devoted to the study of a new class of optimal control problems
governed by the classical Moreau sweeping process with the new feature that the polyhe-
dral moving set is not fixed while controlled by time-dependent functions. The dynamics of
such problems is described by dissipative non-Lipschitzian differential inclusions with state
constraints of equality and inequality types. It makes challenging and difficult their anal-
ysis and optimization. In this paper we establish some existence results for the sweeping
process under consideration and develop the method of discrete approximations that allows
us to strongly approximate, in the W^{1,2} topology, optimal solutions of the continuous-type
sweeping process by their discrete counterparts
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