Minimization problems involving polyconvex integrands
This thesis is mainly concerned with problems in the areas of the Calculus of Variations and Partial Differential Equations (PDEs). The properties of the functional to minimize with respect to the given topology play an important role in the existence of minimizers of integral problems. We will in...
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Format: | Others |
Language: | en_US |
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Georgia Institute of Technology
2015
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Online Access: | http://hdl.handle.net/1853/53901 |
Summary: | This thesis is mainly concerned with problems in the areas of the Calculus of Variations and
Partial Differential Equations (PDEs).
The properties of the functional to minimize with respect to the given topology
play an important role in the existence of minimizers of integral problems. We will introduce
the important concepts of quasiconvexity and polyconvexity. Inspired by finite element methods from Numerical Analysis, we introduce a perturbed problem which has some surprising uniqueness properties. |
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