Displaying similar documents to “On the set of values of the system { f ( z 1 ) , ⋯ , f ( z n ) } in the class of typically real functions.”

Derivative of the Donsker delta functionals

Herry Pribawanto Suryawan (2019)

Mathematica Bohemica

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We prove that derivatives of any finite order of Donsker's delta functionals are well-defined elements in the space of Hida distributions. We also show the convergence to the derivative of Donsker's delta functionals of two different approximations. Finally, we present an existence result of finite product and infinite series of the derivative of the Donsker delta functionals.

On the lower semicontinuity of supremal functionals defined on measures

Michele Gori (2006)

Bollettino dell'Unione Matematica Italiana

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In this paper we consider two particular classes of supremal functionals defined on Radon measures and we find necessary and sufficient conditions for their lower semicontinuity with respect to the weak* convergence. Some applications to the minimization of functionals defined on BV are presented.

The (sub/super)additivity assertion of Choquet

Heinz König (2003)

Studia Mathematica

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The assertion in question comes from the short final section in Theory of capacities of Choquet (1953/54), in connection with his prototype of the subsequent Choquet integral. The problem was whether and when this operation is additive. Choquet had the much more abstract idea that all functionals in a certain wide class must be subadditive, and similarly for superadditivity. His treatment of this point was more like an outline, and his proof limited to a rather narrow special case. Thus...

The relaxation of the Signorini problem for polyconvex functionals with linear growth at infinity

Jarosław L. Bojarski (2005)

Applicationes Mathematicae

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The aim of this paper is to study the unilateral contact condition (Signorini problem) for polyconvex functionals with linear growth at infinity. We find the lower semicontinuous relaxation of the original functional (defined over a subset of the space of bounded variations BV(Ω)) and we prove the existence theorem. Moreover, we discuss the Winkler unilateral contact condition. As an application, we show a few examples of elastic-plastic potentials for finite displacements.