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Approximations by regular sets and Wiener solutions in metric spaces

Anders Björn, Jana Björn (2007)

Commentationes Mathematicae Universitatis Carolinae

Let X be a complete metric space equipped with a doubling Borel measure supporting a weak Poincaré inequality. We show that open subsets of X can be approximated by regular sets. This has applications in nonlinear potential theory on metric spaces. In particular it makes it possible to define Wiener solutions of the Dirichlet problem for p -harmonic functions and to show that they coincide with three other notions of generalized solutions.

Approximations of parabolic variational inequalities

Alexander Ženíšek (1985)

Aplikace matematiky

The paper deals with an initial problem of a parabolic variational inequality whichcontains a nonlinear elliptic form a ( v , w ) having a potential J ( v ) , which is twice G -differentiable at arbitrary v H 1 ( Ω ) . This property of a ( v , w ) makes it possible to prove convergence of an approximate solution defined by a linearized scheme which is fully discretized - in space by the finite elements method and in time by a one-step finite-difference method. Strong convergence of the approximate solution is proved without any regularity...

A-Quasiconvexity: Relaxation and Homogenization

Andrea Braides, Irene Fonseca, Giovanni Leoni (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Integral representation of relaxed energies and of Γ-limits of functionals ( u , v ) Ω f ( x , u ( x ) , v ( x ) ) d x are obtained when sequences of fields v may develop oscillations and are constrained to satisfy a system of first order linear partial differential equations. This framework includes the treatement of divergence-free fields, Maxwell's equations in micromagnetics, and curl-free fields. In the latter case classical relaxation theorems in W1,p, are recovered.

Asignación de recursos Max-Min: propiedades y algoritmos.

Amparo Mármol Conde, Blas Pelegrín Pelegrín (1991)

Trabajos de Investigación Operativa

Este trabajo trata el problema de asignación de recursos cuando el objetivo es maximizar la mínima recompensa y las funciones recompensa son continuas y estrictamente crecientes. Se estudian diferentes propiedades que conducen a algoritmos que permiten de forma eficiente la resolución de gran variedad de problemas de esta naturaleza, tanto con variables continuas como discretas.

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