We consider the minimization of a functional of the calculus of variations, under assumptions that are diffeomorphism invariant. In particular, a nonuniform coercivity condition needs to be considered. We show that the direct methods of the calculus of variations can be applied in a generalized Sobolev space, which is in turn diffeomorphism invariant. Under a suitable (invariant) assumption, the minima in this larger space belong to a usual Sobolev space and are bounded.

Degiovanni, M., Marzocchi, M., Diffeomorphism Invariant Minimization of Functionals with Nonuniform Coercivity, <<MATHEMATICS>>, 2025; 13 (3): 1-23. [doi:10.3390/math13030426] [https://hdl.handle.net/10807/309416]

Diffeomorphism Invariant Minimization of Functionals with Nonuniform Coercivity

Degiovanni, Marco
Primo
;
Marzocchi, Marco
Secondo
2025

Abstract

We consider the minimization of a functional of the calculus of variations, under assumptions that are diffeomorphism invariant. In particular, a nonuniform coercivity condition needs to be considered. We show that the direct methods of the calculus of variations can be applied in a generalized Sobolev space, which is in turn diffeomorphism invariant. Under a suitable (invariant) assumption, the minima in this larger space belong to a usual Sobolev space and are bounded.
2025
Inglese
Degiovanni, M., Marzocchi, M., Diffeomorphism Invariant Minimization of Functionals with Nonuniform Coercivity, <<MATHEMATICS>>, 2025; 13 (3): 1-23. [doi:10.3390/math13030426] [https://hdl.handle.net/10807/309416]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/309416
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