The variable exponent Sobolev capacity and quasi-fine properties of Sobolev functions in the case \(p^-=1\)

DOI10.1016/j.jmaa.2013.08.063zbMath1347.46025OpenAlexW1976339245MaRDI QIDQ2019089

Matti Nuortio, Heikki Hakkarainen

Publication date: 27 March 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2013.08.063

zbMATH Keywords

quasi-continuityvariable exponentSobolev capacityLebesgue pointslimiting case

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items (3)

The variable exponent BV-Sobolev capacity ⋮ Removability of zero modular capacity sets ⋮ Differentiability of logarithmic Besov functions in terms of capacities

Cites Work

• The variable exponent BV-Sobolev capacity
• Lebesgue and Sobolev spaces with variable exponents
• Nonlinear potential theory on metric spaces
• The Dirichlet energy integral and variable exponent Sobolev spaces with zero boundary values
• Some properties of variable Sobolev capacity
• Overview of differential equations with non-standard growth
• Lebesgue points for Sobolev functions on metric spaces.
• Sobolev capacity of the space \(W^{1,p(\cdot)} (\mathbb{R}^n)\)
• Hölder quasicontinuity in variable exponent Sobolev spaces
• On the density of smooth functions in Sobolev-Orlicz spaces
• Density of smooth functions in W ^{k, p(x)} ( Ω )
• On the σ-class generated by open balls
• On a progress in the theory of lebesgue spaces with variable exponent: maximal and singular operators
• Continuity at boundary points of solutions of quasilinear elliptic equations with a non-standard growth condition
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