A Sobolev-like inequality for the Dirac operator
Abstract
Description
In this article, we prove a Sobolev-like inequality for the Dirac operator on closed compact Riemannian spin manifolds with a nearly optimal Sobolev constant. As an application, we give a criterion for the existence of solutions to a nonlinear equation with critical Sobolev exponent involving the Dirac operator. We finally specify a case where this equation can be solved.
some typos corrected, the introduction has been rewritten and several references has been added, to appear in Journal of Functional Analysis
some typos corrected, the introduction has been rewritten and several references has been added, to appear in Journal of Functional Analysis