Monotone and pseudomonotone operators with applications to variational problems

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dc.contributor.advisorEbobisse Bille, Francoisen_ZA
dc.contributor.authorAlexander, Byron Josephen_ZA
dc.date.accessioned2015-11-30T13:11:56Z
dc.date.available2015-11-30T13:11:56Z
dc.date.issued2015en_ZA
dc.descriptionIncludes bibliographical referencesen_ZA
dc.description.abstractThis work is primarily concerned with investigating how monotone and pseudomonotone operators between Banach spaces are used to prove the existence of solutions to nonlinear elliptic boundary value problems. A well-known approach to solving nonlinear elliptic boundary value problems is to reformulate them as equations of the form A (u) = f, where A is a monotone or pseudomonotone operator from a Sobolev space to its dual. We seek to study the abstract theory which underpins this approach and proves the existence of a solution to the equation A (u) = f, implying the existence of a weak solution to the elliptic boundary value problem. Further, we examine properties of monotone and pseudomonotone operators, with an emphasis on a characterization, which involves the latter, and establishes a connection between the operator and the principal part of a partial differential equation. In addition, results relating monotone and pseudomonotone operators with variational inequalities are explored.en_ZA
dc.identifier.apacitationAlexander, B. J. (2015). <i>Monotone and pseudomonotone operators with applications to variational problems</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/15464en_ZA
dc.identifier.chicagocitationAlexander, Byron Joseph. <i>"Monotone and pseudomonotone operators with applications to variational problems."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2015. http://hdl.handle.net/11427/15464en_ZA
dc.identifier.citationAlexander, B. 2015. Monotone and pseudomonotone operators with applications to variational problems. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Alexander, Byron Joseph AB - This work is primarily concerned with investigating how monotone and pseudomonotone operators between Banach spaces are used to prove the existence of solutions to nonlinear elliptic boundary value problems. A well-known approach to solving nonlinear elliptic boundary value problems is to reformulate them as equations of the form A (u) = f, where A is a monotone or pseudomonotone operator from a Sobolev space to its dual. We seek to study the abstract theory which underpins this approach and proves the existence of a solution to the equation A (u) = f, implying the existence of a weak solution to the elliptic boundary value problem. Further, we examine properties of monotone and pseudomonotone operators, with an emphasis on a characterization, which involves the latter, and establishes a connection between the operator and the principal part of a partial differential equation. In addition, results relating monotone and pseudomonotone operators with variational inequalities are explored. DA - 2015 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2015 T1 - Monotone and pseudomonotone operators with applications to variational problems TI - Monotone and pseudomonotone operators with applications to variational problems UR - http://hdl.handle.net/11427/15464 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/15464
dc.identifier.vancouvercitationAlexander BJ. Monotone and pseudomonotone operators with applications to variational problems. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2015 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/15464en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematics and Applied Mathematicsen_ZA
dc.titleMonotone and pseudomonotone operators with applications to variational problemsen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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