Pavel Krejčí (2001)
Applications of Mathematics
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It is known that the vector stop operator with a convex closed characteristic of class is locally Lipschitz continuous in the space of absolutely continuous functions if the unit outward normal mapping is Lipschitz continuous on the boundary of . We prove that in the regular case, this condition is also necessary.
Pavel Krejčí (1991)
Applications of Mathematics
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The recent development of mathematical methods of investigation of problems with hysteresis has shown that the structure of the hysteresis memory plays a substantial role. In this paper we characterize the hysteresis operators which exhibit a memory effect of the Preisach type (memory preserving operators). We investigate their properties (continuity, invertibility) and we establish some relations between special classes of such operators (Preisach, Ishlinskii and Nemytskii operators)....
Aurelian Cernea (2002)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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We prove the existence of viable solutions to the Cauchy problem x” ∈ F(x,x’), x(0) = x₀, x’(0) = y₀, where F is a set-valued map defined on a locally compact set , contained in the Fréchet subdifferential of a ϕ-convex function of order two.
M. A. Fugarolas (2004)
Colloquium Mathematicae
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Let Π₂ be the operator ideal of all absolutely 2-summing operators and let be the identity map of the m-dimensional linear space. We first establish upper estimates for some mixing norms of . Employing these estimates, we study the embedding operators between Besov function spaces as mixing operators. The result obtained is applied to give sufficient conditions under which certain kinds of integral operators, acting on a Besov function space, belong to Π₂; in this context, we also...