Motivated by Ruf-Sani's recent work, we prove an Adams type inequality and a singular Adams type inequality in the whole four-dimensional Euclidean space. As applications of those inequalities, a class of elliptic partial differential equations are considered. Existence of nontrivial weak solutions and multiplicity results are obtained via the mountain-pass theorem and the Ekeland's variational principle. This is a continuation of our previous work about singular Trudinger-Moser type inequality. © 2011 Elsevier Inc.
Yang, Y. (2012). Adams type inequalities and related elliptic partial differential equations in dimension four. Journal of Differential Equations, 252(3), 2266–2295. https://doi.org/10.1016/j.jde.2011.08.027