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

摘要

We prove the existence of minimizers for some constrained variational problems on BV (Omega), 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 Poincare-Sobolev type inequalities.(c) 2022 Elsevier Inc. All rights reserved.