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Miles, Joseph B. Movshovich, Yevgenya E. 2011-05-07T12:20:32Z 2011-05-07T12:20:32Z 10000-01-01 1995 This thesis explores a new approach, begun by Maurice Heins and Jang-Mei Wu, to studying the near-boundary behavior of positive solutions of elliptic DE's by finding surfaces which minimize the integrals of solutions over the family of all closed surfaces or curves tending to the boundary. The inferior limit of integrals over this family is estimated for harmonic functions given by the Cantors measures on the unit circle in terms of the porosity of the Cantor set. The exact lower bound of it for all normalized positive harmonic functions in the unit ball of $R\sp{n}$ is established. Also, its value for the functions given by the Dirac measure on the unit n-sphere is computed. The generalized formula of the surface area element in spherical coordinates for the dimension $n>3$ is derived. Made available in DSpace on 2011-05-07T12:20:32Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9624443.pdf: 1638731 bytes, checksum: 9df6a67d5e7c71693c7f3c78a3ba8811 (MD5) Previous issue date: 1995 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:39:50Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:16:54-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9624443 (UMI)AAI9624443 http://hdl.handle.net/2142/19848 eng Copyright 1995 Movshovich, Yevgenya E. Mathematics Integrals of harmonic functions over curves and surfaces text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.