We show that the singular numbers of single layer potentials on smooth curves asymptotically behave like O(1/n). For the curves with singularities, as long as they contain a smooth sub-arc, the resulting single layer potentials are never trace-class. We provide upper bounds for the operator and the Hilbert-Schmidt norms of single layer potentials on smooth and chord-arc curves. Regarding the injectivity of single layer potentials on planar curves, we prove that among single layer potentials on dilations of a given curve, only one yields a non-injective single layer potential. A criterion for injectivity of single layer potentials on ellipses is given. We establish an isoperimetric inequality for Schatten p−norms of logarithmic potentials over quadrilaterals and its analogue for Newtonian potentials on parallelepipeds.
Identifer | oai:union.ndltd.org:USF/oai:scholarcommons.usf.edu:etd-7641 |
Date | 28 June 2016 |
Creators | Zoalroshd, Seyed |
Publisher | Scholar Commons |
Source Sets | University of South Flordia |
Detected Language | English |
Type | text |
Format | application/pdf |
Source | Graduate Theses and Dissertations |
Rights | default |
Page generated in 0.0011 seconds