Regularity for double phase problems at nearly linear growth

Cristiana De Filippis, Giuseppe Mingione

Minima of functionals of the type $$ w\mapsto \int_Ω\left[\snr{Dw}\log(1+\snr{Dw})+a(x)\snr{Dw}^{q}\right] \dx\,, \quad 0\leq a(\cdot) \in C^{0, α}\,,$$ with $Ω\subset \er^n$, have…