Boundary limits of monotone Sobolev functions with variable exponent on uniform domains in a metric space

DOI10.1007/s13163-014-0154-6zbMath1308.30066OpenAlexW2109340003MaRDI QIDQ2256773

Tetsu Shimomura, Takao Ohno, Toshihide Futamura

Publication date: 20 February 2015

Published in: Revista Matemática Complutense (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13163-014-0154-6

zbMATH Keywords

nontangential limitsLindelöf theoremtangential limitsmonotone Sobolev functions

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Boundary behavior of harmonic functions in higher dimensions (31B25) Analysis on metric spaces (30L99)

Cites Work

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• Lindelöf theorems for monotone Sobolev functions in Orlicz spaces
• Lebesgue and Sobolev spaces with variable exponents
• Nonlinear potential theory on metric spaces
• Sobolev's inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space \(L^{p(\cdot)}(\log L)^{q(\cdot)}\)
• Uniform domains
• Conformal geometry and quasiregular mappings
• Traces of monotone Sobolev functions
• Lindelöf theorems for monotone Sobolev functions on uniform domains
• Boundary limits for bounded quasiregular mappings
• Lindelöf theorems for monotone Sobolev functions with variable exponent
• Sobolev met Poincaré
• Regularity theory and traces of 𝒜-harmonic functions
• Boundary behavior of monotone Sobolev functions on John domains in a metric space
• Traces of monotone functions in weighted Sobolev spaces

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