Trudinger-Moser inequalities on complete noncompact Riemannian manifolds

Details Trudinger-Moser inequalities on complete noncompact Riemannian manifolds Trudinger-Moser inequalities on complete noncompact Riemannian manifolds

2011-12-04

arxiv.org/abs/1112.0724v1

Mathematics

Differential Geometry

37 pages

Scientific paper

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.

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