Characterizations of p-superharmonic functions on metric spaces

Anders Björn. "Characterizations of p-superharmonic functions on metric spaces." Studia Mathematica 169.1 (2005): 45-62. <http://eudml.org/doc/285288>.

@article{AndersBjörn2005,
abstract = {We show the equivalence of some different definitions of p-superharmonic functions given in the literature. We also provide several other characterizations of p-superharmonicity. This is done in complete metric spaces equipped with a doubling measure and supporting a Poincaré inequality. There are many examples of such spaces. A new one given here is the union of a line (with the one-dimensional Lebesgue measure) and a triangle (with a two-dimensional weighted Lebesgue measure). Our results also apply to Cheeger p-superharmonic functions and in the Euclidean setting to 𝓐-superharmonic functions, with the usual assumptions on 𝓐.},
author = {Anders Björn},
journal = {Studia Mathematica},
keywords = {-harmonic function; superminimizer; doubling measure; Poincaré inequality; Dirichlet -regular open sets; -superhamonicity},
language = {eng},
number = {1},
pages = {45-62},
title = {Characterizations of p-superharmonic functions on metric spaces},
url = {http://eudml.org/doc/285288},
volume = {169},
year = {2005},
}

TY - JOUR
AU - Anders Björn
TI - Characterizations of p-superharmonic functions on metric spaces
JO - Studia Mathematica
PY - 2005
VL - 169
IS - 1
SP - 45
EP - 62
AB - We show the equivalence of some different definitions of p-superharmonic functions given in the literature. We also provide several other characterizations of p-superharmonicity. This is done in complete metric spaces equipped with a doubling measure and supporting a Poincaré inequality. There are many examples of such spaces. A new one given here is the union of a line (with the one-dimensional Lebesgue measure) and a triangle (with a two-dimensional weighted Lebesgue measure). Our results also apply to Cheeger p-superharmonic functions and in the Euclidean setting to 𝓐-superharmonic functions, with the usual assumptions on 𝓐.
LA - eng
KW - -harmonic function; superminimizer; doubling measure; Poincaré inequality; Dirichlet -regular open sets; -superhamonicity
UR - http://eudml.org/doc/285288
ER -