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Enclosure theorems for eigenvalues of elliptic operators

University of British Columbia

Enclosure theorems for the eigenvalues and representational formulae for the eigenfunctions of a linear, elliptic, second order partial differential operator will be established for specific domain perturbations to which the classical theory cannot be applied. In particular, the perturbation of n-dimensional Euclidean space E[superscript]n to an n-disk D[subscript]a of radius a is considered in Chapter I and the perturbation of the upper half-space H[superscript]n of E[superscript]n to the upper half of D[subscript]a, S[subscript]a, is discussed in Chapter II. In each case a general self-adjoint boundary condition is adjoined on the bounding surface of the perturbed domain.

Text

2011-09-26

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http://hdl.handle.net/2429/37612

Mathematics

University of British Columbia

Graduate