Classification results for bounded positive solutions to the critical $p$-Laplace equation

Abstract

By providing optimal or nearly optimal integral estimates, we show that every positive, bounded or moderately growing, local weak solution to the critical $p$-Laplace equation in ${\mathbb{R}}^n$, with $n\ge 3$, and whose infimum over a ball behaves properly must be a bubble.

Comments are welcome

References in corpus (3)

• Classification of positive ${\mathcal{D}}^{1,p}({\mathbb{R}}^N)$-solutions to the critical $p$-Laplace equation in ${\mathbb{R}}^N$
• Sharp pointwise estimates for weighted critical $p$-Laplace equations
• On the stability of the critical $p$-Laplace equation