TITLE:
A Note on Sharp Affine Poincaré-Sobolev Inequalities and Exact in Minimization of Zhang’s Energy on Bounded Variation and Exactness
AUTHORS:
Salih Yousuf Mohamed Salih
KEYWORDS:
Affine Energy, Affine Sobolev Inequality, Compactness of Affine Immersion, Constrained Minimization
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.3,
March
30,
2023
ABSTRACT: As for the affine energy, Edir Junior and Ferreira Leite establish the existence of minimizers for particular restricted subcritical and critical variational issues on BV(Ω). Similar functionals exhibit deeper weak* topological traits including lower semicontinuity and affine compactness, and their geometry is non-coercive. Our work also proves the result that extremal functions exist for certain affine Poincaré-Sobolev inequalities.