Regularity for double-phase functionals with nearly linear growth and two modulating coefficients
Bogi Kim, Jehan Oh · Advances in Nonlinear Analysis · 2025
Abstract We deal with non-uniformly elliptic integral functionals w ↦ ∫ c ( x ) ∣ D w ∣ log ( 1 + ∣ D w ∣ ) + a ( x ) ( ∣ D w ∣ 2 + s 2 ) q 2 + 1 d x , w\mapsto \int \left[{\mathfrak{c}}\left(x)| Dw| \log \left(1+| Dw| )+a\left(x){\left({| Dw| }^{2}+{s}^{2})}^{\tfrac{q}{2}}+1\right]{\rm{d}}x, with s ∈ [ 0 , 1 ] s\in \left[0,1] , q > 1 q\gt 1 , 0 ≤ c ( ⋅ ) ≤ Λ , a ( ⋅ ) ≥ 0 0\le {\mathfrak{c}}\left(\cdot )\le \Lambda ,a\left(\cdot )\ge 0 , and a ( x ) + c ( x ) ≥ 1 Λ a\left(x)+{\mathfrak{c}}\left(x)\ge \frac{1}{\Lambda } for some