Estimates of \(p\)-harmonic functions in planar sectors (Q6045825)

The paper deals with \(p\)-harmonic functions in 2-dimensional sectors, for \(p>1\), including the case \(p=\infty\). The authors first obtain estimates for \(p\)-harmonic measures and then they derive growth estimates for \(p\)-sub and \(p\)-superharmonic functions vanishing in suitable sets. One consequence of the result is also an extended version of a classical result of Phragmém-Lindelöf (a generalization of maximum principle for unbounded domains) and a consequent uniqueness result, for domains contained in planar sectors. Finally, in the case \(p=\infty\), the authors show that similar results hold also in \(n\)-dimensional cones (\(n>2\)). The paper also presents an extensive discussion of the relevant literature and gives a review of several well known basic definitions and results related to the \(p\)-Laplace equation.