N-Capacity, N-harmonic radius and N-harmonic transplantation

For the N-Laplacian N on a regular domain the N-Green’s function exists. This allows us to define the N-Robin’s function and the N-harmonic radius. We show their basic properties and extend the method of the harmonic transplantation to that of the N-harmonic transplantation. The method is used to estimate the first eigenvalue of the N-Laplacian N. We also give another proof of the isoperimetric inequality for the N-capacity and give the isoperimetric inequality for the N-harmonic radius. © 2006 Elsevier Inc. All rights reserved