Heat trace asymptotics with singular weight functions II
Michiel van den Berg, Peter Gilkey, Klaus Kirsten
TL;DR
This paper investigates the asymptotic behavior of the heat trace for Laplace-type operators with singular weight functions, deriving formulas for boundary terms considering geometric data and boundary conditions.
Contribution
It provides explicit formulas for the first three boundary terms in heat trace asymptotics with singular weights and mixed boundary conditions, extending previous results.
Findings
Formulas for the first three boundary terms derived
Explicit dependence on geometric data established
Analysis of operators with radial blowup weight functions
Abstract
We study the weighted heat trace asymptotics of an operator of Laplace type with mixed boundary conditions where the weight function exhibits radial blowup. We give formulas for the first three boundary terms in the expansion in terms of geometrical data.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Spectral Theory in Mathematical Physics · Nonlinear Partial Differential Equations