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- W2078984728 abstract "For positive elliptic differential operators Δ, the asymptotic expansion of the heat trace tr(e -tΔ ) and its related zeta function ζ(s, Δ) = tr(Δ -s ) have numerous applications in geometry and physics. This article discusses the general nature of the boundary conditions that must be considered when there is a singular stratum, and presents three examples in which a choice of boundary conditions at the singularity must be made. The first example concerns the signature operator on a manifold with a singular stratum of conic type. The second concerns the Zaremba problem for a nonsingular manifold with smooth boundary, posing Dirichlet conditions on part of the boundary and Neumann conditions on the complement; the intersection of these two regions can be viewed as a singular stratum of conic type, and a boundary condition must be imposed along this stratum. The third example is a one-dimensional manifold where the operator at one end has a singularity like that in conic problems, and the choice of boundary conditions affects not just the residues at the poles of the zeta function, but also the very location of the poles" @default.
- W2078984728 created "2016-06-24" @default.
- W2078984728 creator A5080764515 @default.
- W2078984728 date "2003-05-10" @default.
- W2078984728 modified "2023-09-27" @default.
- W2078984728 title "Heat Kernel Expansions in the Case of Conic Singularities" @default.
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- W2078984728 doi "https://doi.org/10.1142/s0217751x03015659" @default.
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