Gradient estimates and a failure of the mean value principle for p-harmonic functions
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Korte, Riikka; Lahti, Panu; Li, Xining; Shanmugalingam, Nageswari (European Mathematical Society Publishing House, 2019)We study two notions of Dirichlet problem associated with BV energy minimizers (also called functions of least gradient) in bounded domains in metric measure spaces whose measure is doubling and supports a (1, 1)-Poincaré ...
Existence and almost uniqueness for p-harmonic Green functions on bounded domains in metric spaces Björn, Anders; Björn, Jana; Lehrbäck, Juha (Elsevier, 2020)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 if the complement of the domain has positive ...
Coulhon, Thierry; Jiang, Renjin; Koskela, Pekka; Sikora, Adam (Elsevier, 2020)Let (X,d,μ) be a doubling metric measure space endowed with a Dirichlet form E deriving from a “carré du champ”. Assume that (X,d,μ,E) supports a scale-invariant L2-Poincaré inequality. In this article, we study the following ...
Keisala, Jukka (University of Jyväskylä, 2011)
Vesterinen, Päivikki (2015)