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dc.contributor.advisorMitrea, Mariuseng
dc.contributor.authorMayboroda, Svitlanaeng
dc.date.issued2005eng
dc.date.submitted2005 Springeng
dc.descriptionThe entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.eng
dc.descriptionTitle from title screen of research.pdf file viewed on (January 25, 2007)eng
dc.descriptionIncludes bibliographical references.eng
dc.descriptionVita.eng
dc.descriptionThesis (Ph.D.) University of Missouri-Columbia 2005.eng
dc.descriptionDissertations, Academic -- University of Missouri--Columbia -- Mathematics.eng
dc.description.abstractThe aim of this work is to describe the sharp ranges of indices, for which the Poisson problem for Laplacian with Dirichlet or Neumann boundary conditions is well-posed on the scales of Besov and Triebel-Lizorkin spaces on arbitrary Lipschitz domains. The main theorems we prove extend the work of D. Jerison and C. Kenig [JFA, 95], whose methods and results are largely restricted to the case p_ 1, and answer the open problem #3.2.21 on p. 121 in C. Kenig's book in the most complete fashion. When specialized to Hardy spaces, our results provide a solution of a (strengthened form of a) conjecture made by D.-C. Chang, S.Krantz and E. Stein regarding the regularity of the Green potentials on Hardy spaces in Lipschitz domains. The corollaries of our main results include new proofs and various extensions of: Hardy space estimates for Green potentials in convex domains due to V. Adolfsson, B.Dahlberg, S. Fromm, D. Jerison, G.Verchota and T.Wolff and the Lp - Lq estimates for the gradients of Green potentials in Lipschitz domains, due to B. Dahlberg.eng
dc.identifier.merlinb57681065eng
dc.identifier.urihttps://hdl.handle.net/10355/4133
dc.identifier.urihttps://doi.org/10-32469/10355/4133eng
dc.languageEnglisheng
dc.publisherUniversity of Missouri--Columbiaeng
dc.relation.ispartofcommunityUniversity of Missouri--Columbia. Graduate School. Theses and Dissertationseng
dc.rights.licenseThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License. Copyright held by author.
dc.subject.lcshPoisson's equationeng
dc.subject.lcshLipschitz spaceseng
dc.subject.lcshFunctions of complex variableseng
dc.titleThe poisson problem on Lipschitz domainseng
dc.typeThesiseng
thesis.degree.disciplineMathematics (MU)eng
thesis.degree.grantorUniversity of Missouri--Columbiaeng
thesis.degree.levelDoctoraleng
thesis.degree.namePh. D.eng


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