Bloch estimates in non-doubling generalized Orlicz spaces

Abstract

We study minimizers of non-autonomous functionals \begin{align*} \inf_u \int_Ωφ(x,|\nabla u|) \, dx \end{align*} when $\phi$ has generalized Orlicz growth. We consider the case where the upper growth rate of $\phi$ is unbounded and prove the Harnack inequality for minimizers. Our technique is based on "truncating" the function $\phi$ to approximate the minimizer and Harnack estimates with uniform constants via a Bloch estimate for the approximating minimizers.

References in corpus (10)

• Maximal regularity for local minimizers of non-autonomous functionals
• A pocket guide to nonlinear differential equations in the Musielak--Orlicz spaces
• Lipschitz bounds and nonautonomous integrals
• Existence of renormalized solutions to elliptic equation in Musielak-Orlicz space
• The weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth
• Double phase image restoration
• Regularity theory for non-autonomous partial differential equations without Uhlenbeck structure
• Hölder continuity of $\omega$-minimizers of functionals with generalized Orlicz growth
• A flow approach to the Musielak-Orlicz-Gauss image problem
• Renormalized solutions to parabolic equations in time and space dependent anisotropic Musielak-Orlicz spaces in absence of Lavrentiev's phenomenon