Stability estimates for inverse problems of some elliptic equations
dc.contributor.advisor  Bukhgeym, Alexander L.  
dc.contributor.author  Ingle, William Nathan  
dc.date.accessioned  20120619T14:30:21Z  
dc.date.available  20120619T14:30:21Z  
dc.date.copyright  2011  
dc.date.issued  201112  
dc.identifier.other  d11027  
dc.identifier.uri  http://hdl.handle.net/10057/5149  
dc.description  Thesis (Ph.D.)Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics  en_US 
dc.description.abstract  In this dissertation we obtain new Carleman formulas for the solution of the Cauchy problem for equations P u = h, in Ω, uE = f , where E ⊂ ∂Ω and  E  > 0. Our elliptic operator is of the form P = [ [2∂¯ 0 ; 0 2δ ] + A (x), where A is a 2 x 2 matrix. We also obtain estimates for the solution of equation P u = 0 when u is given at a finite number of points, and we prove that nontrivial solutions to the equation can not be small on large portions of the boundary,  Eδ  ≤ c / ln δ−1 , δ ∈ (0, 1), where Eδ = {z ∈ ∂Ω  u(z)  < δ} and  Eδ  is the Lebesgue measure of Eδ . Finding the boundary condition from only a finite number of interior measurements of a domain is interesting both theoretically and practically. For example, when the boundary is physically inaccessible, all measurements must be made within the domain itself, and the conditions on the boundary must be reconstructed. We investigate the problem of recovering a boundary condition of the third kind for the Laplace operator defined on a simply connected domain in the complex plane, when the value of the solution and its gradient are known only for a finite number of interior points.  
dc.format.extent  vii, 69 p.  en 
dc.language.iso  en_US  en_US 
dc.publisher  Wichita State University  en_US 
dc.rights  Copyright William Ingle, 2011. All rights reserved  en 
dc.subject.lcsh  Electronic dissertations  en 
dc.title  Stability estimates for inverse problems of some elliptic equations  en_US 
dc.type  Dissertation  en_US 
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