Adams type inequalities and related elliptic partial differential equations in dimension four

Details Adams type inequalities and related elliptic partial differential equations in dimension four Adams type inequalities and related elliptic partial differential equations in dimension four

2011-05-08

arxiv.org/abs/1105.1528v1

Mathematics

Analysis of PDEs

27 pages

Scientific paper

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.

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