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dc.contributor.advisorVerbitsky, Igor E.eng
dc.contributor.authorJaye, Benjamin Jameseng
dc.date.issued2011eng
dc.date.submitted2011 Springeng
dc.descriptionTitle from PDF of title page (University of Missouri--Columbia, viewed on October 24, 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: Professor Igor E. Verbitskyeng
dc.descriptionIncludes bibliographical references.eng
dc.descriptionVita.eng
dc.descriptionPh. D. University of Missouri--Columbia 2011.eng
dc.descriptionDissertations, Academic -- University of Missouri--Columbia -- Mathematics.eng
dc.description"May 2011"eng
dc.description.abstractThis thesis concerns the study of a class of second order quasilinear elliptic differential operators. For 1 < p < ∞, the model equation we consider is: (1) L(u) = -Δpu - σ∣u∣p-2u Here the potential is a function (or distribution), and the di erential operator pu is the p-Laplacian. Such operators are said to have `natural growth' terms. When p = 2, the operator reduces to the linear time independent Schrödinger operator. We will study the operator under minimal conditions on , where classical regularity theory for the operator L breaks down. Our focus will be on two heavily studied problems: 1. An existence and regularity theory for positive solutions of L(u) = 0, under the sole condition of form boundedness on the real-valued potential : (2) ∣⟨|h|p,σ|⟩ ≤ C ∫Ω |∇h|p dx, for all h ∈ C∞0 (Ω) Here is assumed to lie in the local dual Sobolev space L-41,p'loc(Ω), and the pairing in display (2) is the natural dual pairing. 2. The pointwise behavior of fundamental solutions of the operator L. Here we will be concerned with positive solutions of L(u) = 0 with a prescribed isolated singularity. The techniques developed to attack these two related problems will be quite different in nature. The first problem relies on a study of the doubling properties of nonnegative functions satisfying a weak reverse Hölder inequality, along with certain weak convergence arguments. The second problem is approached via certain nonlinear integral equations involving Wol 's potential, and makes use of tools from non-homogeneous harmonic analysis.eng
dc.format.extentv, 137 pageseng
dc.identifier.oclc872561328eng
dc.identifier.urihttps://hdl.handle.net/10355/15835
dc.identifier.urihttps://doi.org/10.32469/10355/15835eng
dc.languageEnglisheng
dc.publisherUniversity of Missouri--Columbiaeng
dc.relation.ispartofcollectionUniversity of Missouri--Columbia. Graduate School. Theses and Dissertations.eng
dc.subjectpartial differential equationseng
dc.subjectharmonic analysiseng
dc.subjectnonlinear elliptic equationseng
dc.titleNonlinear equations with natural growth termseng
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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