Bounded nonnegative weak solutions to anisotropic parabolic double phase problems with variable growth

Abstract

We study the homogeneous Dirichlet problem for a class of nonlinear anisotropic parabolic double phase equations with nonstandard growth conditions. We prove the existence of a unique nonnegative weak solution in suitable Orlicz-Sobolev spaces, and derive the global boundedness of the weak solution.

Keywords:

• Existence theory
• nonlinear parabolic problems
• nonstandard growth
• regularity theory

2020 Mathematics Subject Classifications:

• 35K55
• 35K65

Disclosure statement

No potential conflict of interest was reported by the author(s).