The weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth

Abstract

We study unbounded weak supersolutions of elliptic partial differential equations with generalized Orlicz (Musielak--Orlicz) growth. We show that they satisfy the weak Harnack inequality with optimal exponent provided that they belong to a suitable Lebesgue or Sobolev space. Furthermore, we establish the sharpness of our central assumptions.

References in corpus (8)

• Regularity for minimizers for functionals of double phase with variable exponents
• Maximal regularity for local minimizers of non-autonomous functionals
• A pocket guide to nonlinear differential equations in the Musielak--Orlicz spaces
• Double phase problems with variable growth
• Multiple solutions of double phase variational problems with variable exponent
• Double phase image restoration
• Hölder continuity of $\omega$-minimizers of functionals with generalized Orlicz growth
• Renormalized solutions to parabolic equations in time and space dependent anisotropic Musielak-Orlicz spaces in absence of Lavrentiev's phenomenon

Cited by in corpus (8)

• Maximal regularity for local minimizers of non-autonomous functionals
• Regularity theory for non-autonomous partial differential equations without Uhlenbeck structure
• Regularity theory for non-autonomous problems with a priori assumptions
• A fundamental condition for harmonic analysis in anisotropic generalized Orlicz spaces
• A revised condition for harmonic analysis in generalized Orlicz spaces on unbounded domains
• Wolff potentials and local behaviour of solutions to measure data elliptic problems with Orlicz growth
• Bloch estimates in non-doubling generalized Orlicz spaces
• Continuity at a boundary point of solutions to quasilinear elliptic equations with generalized Orlicz growth and non-logarithmic conditions