Heat content asymptotics for higher order Laplacians

Abstract Let M be a compact Riemannian manifold with smooth boundary ϖM . We study the heat content asymptotics for higher order Laplacians with boundary conditions of mixed type.

[1]  P. Gilkey.  The spectral geometry of the higher order Laplacian , 1980 .

[2]  P. Gilkey,et al.  Heat content asymptotics for operators of laplace type with Neumann boundary conditions , 1994 .

[3]  Steven G. Krantz,et al.  Invariance Theory Heat Equation and Atiyah Singer Index Theorem , 1995 .

[4]  A. Gray,et al.  Mean-value theorems for Riemannian manifolds , 1982, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[5]  M. van den Berg,et al.  Heat flow out of regions in ℝm , 1989 .

[6]  P. Greiner.  An asymptotic expansion for the heat equation , 1971 .

[7]  V. Gusynin.  Seeley-Gilkey coefficients for fourth-order operators on a riemannian manifold , 1990 .

[8]  H. Weyl.  The Classical Groups , 1939 .

[9]  A. Barvinsky,et al.  The Generalized Schwinger-Dewitt Technique in Gauge Theories and Quantum Gravity , 1985 .

[10]  Peter B. Gilkey,et al.  Heat Content Asymptotics of a Riemannian Manifold with Boundary , 1994 .

[11]  P. Gilkey,et al.  Invariants of the heat equation , 1985 .

[12]  Robert T. Seeley,et al.  THE RESOLVENT OF AN ELLIPTIC BOUNDARY PROBLEM. , 1969 .

[13]  D. Mcavity.  Surface energy from heat content asymptotics , 1993 .

[14]  M. Berg,et al.  Functorality and heat content asymptotics for operators of Laplace type , 1993 .

[15]  S. Minakshisundaram,et al.  Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds , 1949, Canadian Journal of Mathematics.

[16]  S. Desjardins.  ASYMPTOTIC EXPANSIONS FOR THE HEAT CONTENT , 1998 .

[17]  H. Luckock.  Mixed boundary conditions in quantum field theory , 1991 .

[18]  P. Gilkey.  The boundary integrand in the formula for the signature and Euler characteristic of a Riemannian manifold with boundary , 1975 .

[19]  G. Grubb.  On the Functional Calculus of Pseudo-Differential Boundary Problems , 1984 .