Calculus of Variations
Direct method, gamma convergence, and minimizers of functionals.
Calculus of Variations. Direct method, gamma convergence, and minimizers of functionals.
Foundations and canonical references
The standard treatments of calculus of variations approach the subject from complementary angles. Dacorogna, Direct Methods in the Calculus of Variations (2008) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Giaquinta, Calculus of Variations (1996) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for calculus of variations include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2008Direct Methods in the Calculus of Variationsdacorogna-2008
- textbook · primary · 1996Calculus of Variationsgiaquinta-1996, hildebrandt-1996
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