In this section, we prove Theorems 1 and 2 in the case that N≥3. We put emphasis on
the essential difference between 2 dimensions and N dimensions. In the sequel, we denote
ΔNu=div(|∇u|N−2∇u) for any u∈W1,N(RN) (N≥3).
Let ζ:N×R→R be defined as in (6…