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In this article we study metric measure spaces with variable dimension. We consider Lebesgue spaces on these sets, and embeddings of the Riesz potential in these spaces. We also investigate… (More)

- J. Kinnunen, V. Latvala
- 2002

Our main objective is to study the pointwise behaviour of Sobolev functions on a metric measure space. We prove that a Sobolev function has Lebesgue points outside a set of capacity zero if the… (More)

We study energy minimizing properties of the function u = limj!1+ uj , where uj is the solution to the pj (·)- Laplacian Dirichlet problem with prescribed boundary values. Here p: ! (1,1) is a… (More)

- Anders Bjørn, Jana Bjorn, V. Latvala
- 2016

We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space X equipped with a doubling measure supporting a p-Poincare inequality with 1 amp;lt; p amp;lt; infinity,… (More)

We study the balayage related to the supersolutions of the variable exponent p(·)-Laplace equation. We prove the fundamental convergence theorem for the balayage and apply it for proving the Kellogg… (More)

We prove the strong minimum principle for non-negative quasisuperminimizers of the variable exponent Dirichlet energy integral under the assumption that the exponent has modulus of continuity… (More)

- Anders Björn, Jana Björn, V. Latvala
- 2018

We prove the Cartan and Choquet properties for the fine topology on a complete metric space equipped with a doubling measure supporting a p-Poincaré inequality, 1 < p < ∞. We apply these key tools to… (More)

We study the p(¢)-fine continuity in the variable exponent Sobolev spaces under the standard assumptions that p: › ! R is log-Holder continuous and 1 < p i • p + < 1. As a by-product we obtain… (More)

- Peter Harjulehto, P. Hästö, V. Latvala, O. Toivanen
- Appl. Math. Lett.
- 2013

Abstract We study a variable exponent model for image restoration in the case that the exponent attains the critical value one. We prove existence and Γ -convergence. The results answer an open… (More)

Abstract We study properties of the function u = lim λ → ∞ u λ , where u λ is the solution of the min { p ( ⋅ ) , λ } -Laplacian Dirichlet problem with bounded Sobolev boundary function. Here p : Ω →… (More)