Journal of Fixed Point Theory and Applications

, Volume 14, Issue 1, pp 267–298

Neumann heat content asymptotics with singular initial temperature and singular specific heat


  • M. van den Berg
    • School of MathematicsUniversity of Bristol
    • Mathematics DepartmentUniversity of Oregon
  • H. Kang
    • Department of MathematicsKorea Institute for Advanced Study

DOI: 10.1007/s11784-013-0147-y

Cite this article as:
van den Berg, M., Gilkey, P. & Kang, H. J. Fixed Point Theory Appl. (2013) 14: 267. doi:10.1007/s11784-013-0147-y


We study the asymptotic behavior of the heat content on a compact Riemannian manifold with boundary and with singular specific heat and singular initial temperature distributions imposing Robin boundary conditions. Assuming the existence of a complete asymptotic series we determine the first three terms in that series. In addition to the general setting, the interval is studied in detail as are recursion relations among the coefficients and the relationship between the Dirichlet and Robin settings.

Mathematics Subject Classification



Neumann Laplacianheat content asymptoticssingular initial temperature

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© Springer Basel 2013