Trudinger-Moser inequalities on complete noncompact Riemannian manifolds

Abstract

Though Trudinger-Moser inequalities on compact Riemannian manifolds or Euclidean space are well understood, we know little about them on complete noncompact Riemannian manifolds. In this paper, we established respectively necessary condition and sufficient condition under which Trudinger-Moser inequalities hold on complete noncompact Riemannian manifolds. For applications of such inequalities, we obtained existence results for some quasilinear equations with nonlinearity of exponential growth.

37 pages

References in corpus (1)

• A Hardy-Moser-Trudinger inequality

Cited by in corpus (1)

• Min-max level estimate for a singular quasilinear polyharmonic equation in ${\mathbb{R}}^{2m}$