Characterizations of p-superharmonic functions on metric spaces

• Autorzy: Anders Björn
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 49J27: Problems in abstract spaces
• 35J60: Nonlinear elliptic equations
• 31C05: Harmonic, subharmonic, superharmonic functions
• 31C45: Other generalizations (nonlinear potential theory, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 169
• Numer: 1
• Strony: 45-62

Daty

wydano

2005

Twórcy

autor

Anders Björn

• Department of Mathematics, Linköpings universitet, SE-581 83 Linköping, Sweden

Identyfikatory

DOI

10.4064/sm169-1-3