Existence of minimizers of free autonomous variational problems via solvability of constrained ones
| Autor: | Cristina Marcelli, Giovanni Cupini, Marcello Guidorzi |
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| Přispěvatelé: | G. Cupini, M. Guidorzi, C. Marcelli |
| Jazyk: | angličtina |
| Rok vydání: | 2009 |
| Předmět: |
Pure mathematics
Class (set theory) Continuous function Applied Mathematics Mathematical analysis Regular polygon Existence theorem NONCOERCIVE PROBLEMS RELAXATION NONCONVEX PROBLEMS Convexity CONSTRAINED PROBLEMS symbols.namesake symbols AUTONOMOUS LAGRANGIANS Relaxation (approximation) Mathematical Physics Analysis Lagrangian Mathematics |
| Popis: | We consider the following autonomous variational problem minimize { ∫ a b f ( v ( x ) , v ′ ( x ) ) d x : v ∈ W 1 , 1 ( a , b ) , v ( a ) = α , v ( b ) = β } where the Lagrangian f is assumed to be continuous, but not necessarily coercive, nor convex. We show that the existence of the minimum is linked to the solvability of certain constrained variational problems. This allows us to derive existence theorems covering a wide class of nonconvex noncoercive problems. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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