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Lindelöf theorems for monotone Sobolev functions in Orlicz spaces on uniform domains
Author(s) -
Futamura Toshihide,
Shimomura Tetsu
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800014
Subject(s) - mathematics , sobolev space , monotone polygon , type (biology) , lebesgue integration , pure mathematics , domain (mathematical analysis) , function (biology) , boundary (topology) , mathematical analysis , geometry , ecology , evolutionary biology , biology
In this paper, we are concerned with Lindelöf type theorems for monotone (in the sense of Lebesgue) Sobolev functions u on a uniform domain D ⊂ R nsatisfying∫ D| ∇ u ( z ) | n − 1 φ ( | ∇ u ( z ) | ) ω δ D ( z )d z < ∞ ,where ∇ denotes the gradient,δ D ( z )denotes the distance from z to the boundary ∂ D , φ is of log‐type and ω is a weight function satisfying the doubling condition.