Diffeomorphism Invariant Minimization of Functionals with Nonuniform Coercivity

Marco Degiovanni () and Marco Marzocchi
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Marco Degiovanni: Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via della Garzetta 48, 25133 Brescia, Italy
Marco Marzocchi: Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via della Garzetta 48, 25133 Brescia, Italy

Mathematics, 2025, vol. 13, issue 3, 1-23

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.

Keywords: calculus of variations; direct methods; invariance by diffeomorphism; quasilinear elliptic equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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