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• Sharp capacity estimates for annuli in weighted R^n and in metric spaces 

  Björn, Anders; Björn, Jana; Lehrbäck, Juha (Springer Berlin Heidelberg, 2017)

  We obtain estimates for the nonlinear variational capacity of annuli in weighted Rn and in metric spaces. We introduce four different (pointwise) exponent sets, show that they all play fundamental roles for capacity ...

• Notions of Dirichlet problem for functions of least gradient in metric measure spaces 

  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 ...

• Characterisation of upper gradients on the weighted Euclidean space and applications 

  Lučić, Danka; Pasqualetto, Enrico; Rajala, Tapio (Springer, 2021)

  In the context of Euclidean spaces equipped with an arbitrary Radon measure, we prove the equivalence among several different notions of Sobolev space present in the literature and we characterise the minimal weak upper ...

• Quasiadditivity of Variational Capacity 

  Lehrbäck, Juha; Shanmugalingam, Nageswari (Springer Netherlands, 2014)

  We study the quasiadditivity property (a version of superadditivity with a multiplicative constant) of variational capacity in metric spaces with respect to Whitney type covers. We characterize this property in terms of a ...

• Muckenhoupt Ap-properties of Distance Functions and Applications to Hardy-Sobolev -type Inequalities 

  Dyda, Bartłomiej; Ihnatsyeva, Lizaveta; Lehrbäck, Juha; Tuominen, Heli; Vähäkangas, Antti (Springer, 2019)