A Stampacchia-type inequality for a fourth-order elliptic operator on Kähler manifolds and applications

Abstract

In this paper we will prove an integral inequality of Stampacchia-type for a fourth-order elliptic operator on complete and connected Kähler manifolds. Our inequality implies a Hodge–Kodaira orthogonal decomposition for the Sobolev-type space Wp,q(X). In particular we will able to prove, under suitable topological conditions on the manifold X, the existence of an isomorphism between the Aeppli groups Λ_p,q_(X) and the groups Hp,q(X) of all global harmonic forms of bidegree (p,q).