Choquet integrals in potential theory.

Adams, David R.. "Choquet integrals in potential theory.." Publicacions Matemàtiques 42.1 (1998): 3-66. <http://eudml.org/doc/41337>.

@article{Adams1998,
abstract = {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.},
author = {Adams, David R.},
journal = {Publicacions Matemàtiques},
keywords = {Teoría del potencial; Espacios de funciones; Ecuaciones diferenciales en derivadas parciales; Capacidad; Espacios de Sobolev; Integrales singulares; Problema elíptico; Choquet integral; Choquet space; Hausdorff capacity; Bessel capacity; obstacle problem for the -Laplace operator; differentiation},
language = {eng},
number = {1},
pages = {3-66},
title = {Choquet integrals in potential theory.},
url = {http://eudml.org/doc/41337},
volume = {42},
year = {1998},
}

TY - JOUR
AU - Adams, David R.
TI - Choquet integrals in potential theory.
JO - Publicacions Matemàtiques
PY - 1998
VL - 42
IS - 1
SP - 3
EP - 66
AB - 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.
LA - eng
KW - Teoría del potencial; Espacios de funciones; Ecuaciones diferenciales en derivadas parciales; Capacidad; Espacios de Sobolev; Integrales singulares; Problema elíptico; Choquet integral; Choquet space; Hausdorff capacity; Bessel capacity; obstacle problem for the -Laplace operator; differentiation
UR - http://eudml.org/doc/41337
ER -