Adams' Inequality with the Exact Growth Condition in ℝ4

Abstract

Adams' inequality is an extension of the Trudinger‐Moser inequality to the case when the Sobolev space considered has more than one derivative. The goal of this paper is to give the optimal growth rate of the exponential‐type function in Adams' inequality when the problem is considered in the whole space ℝ4. © 2014 Wiley Periodicals, Inc.