Boundary-Value Problems for the Squared Laplace Operator
Abstract
The squared Laplace operator acting on symmetric rank-two tensor fields is studied on a (flat) Riemannian manifold with smooth boundary. Symmetry of this fourth-order elliptic operator is obtained provided that such tensor fields and their first (or second) normal derivatives are set to zero at the boundary. Strong ellipticity of the resulting boundary-value problems is also proved. Mixed boundary conditions are eventually studied which involve complementary projectors and tangential differential operators. In such a case, strong ellipticity is guaranteed if a pair of matrices are non-degenerate. These results find application to the analysis of quantum field theories on manifolds with boundary.
Keywords
Cite
@article{arxiv.hep-th/9809031,
title = {Boundary-Value Problems for the Squared Laplace Operator},
author = {Giampiero Esposito},
journal= {arXiv preprint arXiv:hep-th/9809031},
year = {2007}
}
Comments
22 pages, plain Tex. In the revised version, section 5 has been amended