Variational Convex Analysis

This 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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2009

Author dc:creator

• Botelho, Fabio Silva

Chair dc:contributor.committeechair

• Rogers, Robert C.

Committee members dc:contributor.committeemember

• Hagedorn, George A.
• Thomson, James E.
• Borggaard, Jeffrey T.

• duality
• convex formulations
• Banach spaces
• calculus of variations

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-07212009-112235

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/28351