\(N\)-capacity, \(N\)-harmonic radius and \(N\)-harmonic transplantation
The method of harmonic transplantation was introduced by \textit{J. Hersch} [Comment. Math. Helv. 44, 354--366 (1969; Zbl 0175.12002)]. This method gives upper bounds for domain functionals whereas symmetrization gives lower bounds. The author generalizes this method to the case of \(n\)-harmonic functions defined on regular domains. The \(n\)-Robin function and the \(n\)-harmonic radius are introduced and their basic properties given. A new proof for the isoperimetric inequality for the \(n\)-capacity is given and the isoperimetric inequality for the \(n\)-harmonic radius is proved.
scientific article; zbMATH DE number 5083266
scientific article