Minimization to the Zhang's energy on BV(Ω) and sharp affine Poincaré-Sobolev inequalities

We prove the existence of minimizers for some constrained variational problems on BV(Ω), under subcritical and critical restrictions, involving the affine energy introduced by Zhang in [50]. Related functionals have non-coercive geometry and properties like lower semicontinuity and affine compactnes...

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Veröffentlicht in:Journal of functional analysis 2022-11, Vol.283 (10), p.109646, Article 109646
Hauptverfasser: Leite, Edir Junior Ferreira, Montenegro, Marcos
Format: Artikel
Sprache:eng
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Zusammenfassung:We prove the existence of minimizers for some constrained variational problems on BV(Ω), under subcritical and critical restrictions, involving the affine energy introduced by Zhang in [50]. Related functionals have non-coercive geometry and properties like lower semicontinuity and affine compactness are deeper in the weak* topology. As a by-product of our developments, extremal functions are shown to exist for various affine Poincaré-Sobolev type inequalities.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2022.109646