Abstract
Three of the fundamental issues in the calculus of variations are existence, necessary conditions, and regularity of the solution. The name of Tonelli is usually associated with the first of these, but in fact he contributed to all three. This article reviews the interplay amongst these issues and Tonelli's results concerning them, and also goes on to describe new discoveries which deepen and complete our understanding of the basic problem in the calculus of variations.
Keywords
- Periodic Solution
- Euler Equation
- Recent Progress
- Minimal Period
- Regularity Theorem
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© 1986 Springer-Verlag
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Clarke, F.H. (1986). Tonelli's regurarity theory in the calculus of variations: Recent progress. In: Conti, R., De Giorgi, E., Giannessi, F. (eds) Optimization and Related Fields. Lecture Notes in Mathematics, vol 1190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076705
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DOI: https://doi.org/10.1007/BFb0076705
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