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Continuation of solutions of elliptic systems from discrete sets with application to geometry of surfaces
Domme, Cristina Camelia
Domme, Cristina Camelia
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2018-07
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Electronic dissertation
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Abstract
We obtain new estimates of stability for continuation of solutions of elliptic inequali-
ties | ∂u|2 < = a|u|2 from finite discrete sets. For this we use Hormander's type of Carleman
estimates for ∂-bar with boundary terms and a special weight function equal to the linear com-bination of Green's functions with singularities at points where our function is given. To
estimate functions in a given domain we use not only the classical Blaschke partial sum Sn
but we also introduce a new sequence of numbers Mn which gives us better estimates in the
case of a finite number of observations.
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Thesis (M.S.)-- Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics
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Wichita State University
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Copyright 2018 by Cristina Camelia Domme All Rights Reserved