[-] Show simple item record

dc.contributor.advisorHofmann, Steve, 1958-eng
dc.contributor.authorMourgoglou, Michaileng
dc.date.issued2011eng
dc.date.submitted2011 Summereng
dc.description"July 2011"eng
dc.descriptionTitle from PDF of title page (University of Missouri--Columbia, viewed on May 18, 2012).eng
dc.descriptionThe entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.eng
dc.descriptionDissertation advisor: Dr. Steven Hofmanneng
dc.descriptionVita.eng
dc.descriptionIncludes bibliographical references.eng
dc.descriptionDissertations, Academic -- University of Missouri--Columbia -- Mathematics.eng
dc.description.abstractWe consider divergence form elliptic equations Lu := ∇ • (A∇u) = 0 in the half space ℝn+1+ := {(x,t)∈ ℝn x (0,∞)}, whose coeffi cient matrix A is complex elliptic, bounded and measurable. In addition, we suppose that A satisfi es some additional regularity in the direction transverse to the boundary, namely that the discrepancy A(x,t) - A(x,0) satis fies a Carleson measure condition of Feff erman-Kenig-Pipher type, with small Carleson norm. Under these conditions, we obtain solvability of the Dirichlet problem for L, with data in Λα (ℝn) (which is defi ned to be BMO(ℝn) when α = 0 and the space of Holder continuous functions C α(ℝn) when α ∈(0, 1)) for α < α0, where 0 is the De Giorgi-Nash exponent, and solvability of the Neumann and Regularity problems, with data in the spaces Hp(Rn) and H1,p(ℝn) respectively, for p ∈ ( n/n+α 0, 1], assuming that we have bounded Layer Potentials in L2(ℝn) and invertible Layer Potentials in Λα (ℝn) and Hp(ℝn) for the t-independent operator L0 := -∇ • (A( • ,0)∇).eng
dc.format.extentiv, 76 pageseng
dc.identifier.oclc872561136eng
dc.identifier.urihttps://hdl.handle.net/10355/14218
dc.identifier.urihttps://doi.org/10.32469/10355/14218eng
dc.languageEnglisheng
dc.publisherUniversity of Missouri--Columbiaeng
dc.relation.ispartofcollectionUniversity of Missouri--Columbia. Graduate School. Theses and Dissertations.eng
dc.subjectharmonic analysiseng
dc.subjectHardy spaceeng
dc.subjectpartial differential equationseng
dc.subjectcomplex coefficientseng
dc.titleEndpoint solvability results for divergence form, complex elliptic equationseng
dc.typeThesiseng
thesis.degree.disciplineMathematics (MU)eng
thesis.degree.grantorUniversity of Missouri--Columbiaeng
thesis.degree.levelDoctoraleng
thesis.degree.namePh. D.eng


Files in this item

[PDF]
[PDF]
[PDF]

This item appears in the following Collection(s)

[-] Show simple item record