Abstract The asymptotic expansions of the trace of the heat kernel for small positive t, where {λ_{v}} are the eigenvalues of the negative Laplacian in R^{n} (n=2 or 3), are studied for a general annular bounded domain Ω with a smooth inner boundary and a smooth outer boundary , where a finite number of piecewise smooth Robin boundary conditions on the components Γ_{j} (j=1,..., k) of and on the components Γ_{j}(j=k+1,...,m) of are considered such that and and where the coeffcients γ_{j}(j=1,...,m) are piecewise smooth positive functions. Some applications of Θ(t) for an ideal gas enclosed in the general annular bounded domain Ω are given. Further results are also obtained.

E. M. E. ZAYED. Asymptotic Expansions of the Heat Kernel of the Laplacian for General Annular Bounded Domains with Robin Boundary Conditions: Further Results[J]. Acta Mathematica Sinica, English Series, 2003, 19(4): 679-694.

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