Anders Björn

collaborators

4 papers

math.AP2019

Existence and almost uniqueness for $p$ -harmonic Green functions on bounded domains in metric spaces

Anders Björn, Jana Björn, Juha Lehrbäck

We study ( $p$ -harmonic) singular functions, defined by means of upper gradients, in bounded domains in metric measure spaces. It is shown that singular functions exist if and only…

math.AP2019

Boundary regularity for $p$ -harmonic functions and solutions of obstacle problems on unbounded sets in metric spaces

Anders Björn, Daniel Hansevi

The theory of boundary regularity for $p$ -harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a $p$ -Poincaré inequali…

math.MG2018

The Liouville theorem for $p$ -harmonic functions and quasiminimizers with finite energy

Anders Björn, Jana Björn, Nageswari Shanmugalingam

We show that, under certain geometric conditions, there are no nonconstant quasiminimizers with finite $p$ th power energy in a (not necessarily complete) metric measure space equip…

math.MG2018

Locally $p$ -admissible measures on $R$

Anders Bjorn, Jana Bjorn, Nageswari Shanmugalingam

In this note we show that locally $p$ -admissible measures on $R$ necessarily come from local Muckenhoupt $A_{p}$ weights. In the proof we employ the corresponding characteri…

Existence and almost uniqueness for p-harmonic Green functions on bounded domains in metric spaces

Boundary regularity for p-harmonic functions and solutions of obstacle problems on unbounded sets in metric spaces

The Liouville theorem for p-harmonic functions and quasiminimizers with finite energy

Locally p-admissible measures on R

Existence and almost uniqueness for $p$ -harmonic Green functions on bounded domains in metric spaces

Boundary regularity for $p$ -harmonic functions and solutions of obstacle problems on unbounded sets in metric spaces

The Liouville theorem for $p$ -harmonic functions and quasiminimizers with finite energy

Locally $p$ -admissible measures on $R$