Choquet integrals in potential theory

Autores: David R. Adams
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 42, Nº 1, 1998, págs. 3-66
Idioma: inglés
DOI: 10.5565/publmat_42198_01
Títulos paralelos:
- Integrales de Choquet en teoría del potencial
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Resumen
- This is a survey of various applications of the notion of the Choquet integral to questions in Potential Theory, i.e. the integral of a function with respect to a non-additive set function on subsets of Euclidean $n$-space, capacity. The Choquet integral is, in a sense, a nonlinear extension of the standard Lebesgue integral with respect to the linear set function, measure. Applications include an integration principle for potentials, inequalities for maximal functions, stability for solutions to obstacle problems, and a refined notion of pointwise differentiation of Sobolev functions.