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 |
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Hauptverfasser: | , |
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. |
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ISSN: | 0022-1236 1096-0783 |
DOI: | 10.1016/j.jfa.2022.109646 |