Variational Convex Analysis

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dc.contributor.authorBotelho, Fabio Silvaen
dc.contributor.committeechairRogers, Robert C.en
dc.contributor.committeememberHagedorn, George A.en
dc.contributor.committeememberThomson, James E.en
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:14:10Zen
dc.date.adate2009-08-03en
dc.date.available2014-03-14T20:14:10Zen
dc.date.issued2009-07-15en
dc.date.rdate2009-08-03en
dc.date.sdate2009-07-21en
dc.description.abstractThis work develops theoretical and applied results for variational convex analysis. First we present the basic tools of analysis necessary to develop the core theory and applications. New results concerning duality principles for systems originally modeled by non-linear differential equations are shown in chapters 9 to 17. A key aspect of this work is that although the original problems are non-linear with corresponding non-convex variational formulations, the dual formulations obtained are almost always concave and amenable to numerical computations. When the primal problem has no solution in the classical sense, the solution of dual problem is a weak limit of minimizing sequences, and the evaluation of such average behavior is important in many practical applications. Among the results we highlight the dual formulations for micro-magnetism, phase transition models, composites in elasticity and conductivity and others. To summarize, in the present work we introduce convex analysis as an interesting alternative approach for the understanding and computation of some important problems in the modern calculus of variations.en
dc.description.degreePh. D.en
dc.identifier.otheretd-07212009-112235en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-07212009-112235/en
dc.identifier.urihttp://hdl.handle.net/10919/28351en
dc.publisherVirginia Techen
dc.relation.haspartThesisFabio.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectdualityen
dc.subjectconvex formulationsen
dc.subjectBanach spacesen
dc.subjectcalculus of variationsen
dc.titleVariational Convex Analysisen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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