We prove the local boundedness of local weak solutions to the parabolic equation \ ₓu\, =\, ₈=₁^nₗ_₈[ (uₗ_₈-δ₈) +^p-1uₗ_₈ uₗ_{₈}\, \, \, \, \, \, \, \, \, \, in\, \, \, Ωₓ=Ω (0, T]\, , \] where Ω is a bounded domain in R^n with n2, p2, δ₁, , δ₍ are non-negative numbers and (\, \, ) + denotes the positive part. The main novelty here is that the above equation combines an orthotropic structure with a strongly degenerate behavior. The core result of this paper thus extends a classical boundedness theorem, originally proved for the parabolic p-Laplacian, to a widely degenerate anisotropic setting. As a byproduct, we also obtain the local boundedness of local weak solutions to the isotropic counterpart of the above equation.
Ambrosio et al. (Fri,) studied this question.