Potential Analysis

, Volume 26, Issue 3, pp 225–254

Heat Content Asymptotics for Riemannian Manifolds with Zaremba Boundary Conditions

  • M. van den Berg
  • P. Gilkey
  • K. Kirsten
  • V. A. Kozlov

DOI: 10.1007/s11118-005-9001-1

Cite this article as:
van den Berg, M., Gilkey, P., Kirsten, K. et al. Potential Anal (2007) 26: 225. doi:10.1007/s11118-005-9001-1


The existence of a full asymptotic expansion for the heat content asymptotics of an operator of Laplace type with classical Zaremba boundary conditions on a smooth manifold is established. The first three coefficients in this asymptotic expansion are determined in terms of geometric invariants; partial information is obtained about the fourth coefficient.

Key words

Dirichlet boundary conditions heat content asymptotics N/D problem Robin boundary conditions Zaremba problem 

Mathematics Subject Classifications (2000)

58J35 35P99 

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • M. van den Berg
    • 1
  • P. Gilkey
    • 2
  • K. Kirsten
    • 3
  • V. A. Kozlov
    • 4
  1. 1.Department of MathematicsUniversity of BristolBristolUK
  2. 2.Mathematics DepartmentUniversity of OregonEugeneUSA
  3. 3.Department of MathematicsBaylor UniversityWacoUSA
  4. 4.Mathematics DepartmentLinköping UniversityLinköpingSweden