On hearing the shape of a bounded domain with Robin boundary conditions |
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Authors: | Zayed EME |
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Institution: |
Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt
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Abstract: | The asymptotic expansions of the trace of the heat kernel (t)= sum ]j=1 exp(-tj) for small positive t, where {j} j=1 arethe eigenvalues of the negative Laplacian -n = -sum ]nk=1 (/xk)2in Rn (n = 2 or 3), are studied for a general multiply connectedbounded domain which is surrounded by simply connected boundeddomains i with smooth boundaries i (i = 1,...,m), where smoothfunctions Yi (i = 1,...,m) are assuming the Robin boundary conditions(ni + Yi) = 0 on i. Here /ni denote differentiations along theinward-pointing normals to i (i = 1,...,m). Some applicationsof an ideal gas enclosed in the multiply connected bounded containerwith Neumann or Robin boundary conditions are given. |
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