Lindelöf theorems for monotone Sobolev functions in Orlicz spaces. (English) Zbl 1309.31007

A continuous function \(u\) in \(B = \{ x\in R^n: \;|x| <1 \}\) is called monotone if \[ \max_{\overline{D}} u = \max_{\partial D} u, \qquad \min_{\overline{D}} u = \min_{\partial D} u, \] for any domain \(D\) with \(D \subset \overline{B}\). The paper deals with the Lindelöf problem asking for conditions ensuring that \(u\) has tangential and nontangential limits at \(\xi\) with \(|\xi| =1\).


31B25 Boundary behavior of harmonic functions in higher dimensions
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Full Text: Euclid


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