Boundary-Value Problems for the Squared Laplace Operator

Details Boundary-Value Problems for the Squared Laplace Operator Boundary-Value Problems for the Squared Laplace Operator

1998-09-04

arxiv.org/abs/hep-th/9809031v3

Nuovo Cim. B114 (1999) 1029-1048; Erratum-ibid. B115 (2000) 1355

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, plain Tex. In the revised version, section 5 has been amended

Scientific paper

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.

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