On some nonlinear partial differential equations involving the p‐Laplacian and critical Sobolev trace maps.

In this article, we study some partial differential equations with Neumann nonlinear boundary conditions, related to the problem of the best constant from W^{1,p}(\varOmega) to L^{p^\star}(\curpartial\varOmega), where p^\star is the critical Sobolev exponent for the embedding of W^{1,p}(\varOmega) into L^{q}(\curpartial\varOmega) (\varOmega is a bounded \mathcal{C}^1 open set and p<N). [ABSTRACT FROM AUTHOR]