Regularity for double phase problems at nearly linear growth

Abstract

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 locally Hölder continuous gradient provided $1<q<1+\alpha /n$.

50 pages

References in corpus (2)

• Regularity for Orlicz phase problems
• On global absence of Lavrentiev gap for functionals with (p,q)-growth

Cited by in corpus (5)

• Regularity for multi-phase problems at nearly linear growth
• Lipschitz bounds for nonuniformly elliptic integral functionals in the plane
• On the singular set of $\mathrm{BV}$ minimizers for non-autonomous functionals
• Local and global $C^{1,\beta }$-regularity for uniformly elliptic quasilinear equations of $p$-Laplace and Orlicz-Laplace type
• Monotone approximation of differentiable convex functions with applications to general minimization problems