Regularity of minimizers for double phase functionals of borderline case with variable exponents
Maria Alessandra Ragusa, Atsushi Tachikawa · Advances in Nonlinear Analysis · 2024
Abstract The aim of this article is to study regularity properties of a local minimizer of a double phase functional of type ℱ ( u ) ≔ ∫ Ω ( ∣ D u ∣ p ( x ) + a ( x ) ∣ D u ∣ p ( x ) log ( e + ∣ D u ∣ ) ) d x , {\mathcal{ {\mathcal F} }}\left(u):= \mathop{\int }\limits_{\Omega }({| Du| }^{p\left(x)}+a\left(x){| Du| }^{p\left(x)}\log \left(e+| Du| )){\rm{d}}x, being p ( x ) , a ( x ) p\left(x),a\left(x) log-continuous functions with p ( x ) > 1 p\left(x)\gt 1 , a ≥ 0 a\ge 0 . Double phase functionals ∫ ( ∣ D u ∣ p + a ( x ) ∣ D u ∣