Abstract
Abstract We consider a quasilinear degenerate parabolic equation driven by the orthotropic p-Laplacian. We prove that local weak solutions are locally Lipschitz continuous in the spatial variable, uniformly in time.
Highlights
1.1 Aim of the paperLet Ω ⊂ RN be an open bounded set and I ⊂ R an open bounded interval
We consider a quasilinear degenerate parabolic equation driven by the orthotropic p-Laplacian
We prove that local weak solutions are locally Lipschitz continuous in the spatial variable, uniformly in time
Summary
We study the gradient regularity of local weak solutions to the following parabolic equation: N ut = ∑(|uxi |p−2 uxi )xi i=1 in I × Ω. Without any attempt to completeness, we can just mention some classical references [8, 9, 12, 15, 28], up to the most recent contributions on the subject, given by [2, 18, 19], among others None of these results apply to our equation (1.1). The main goal of the present paper is to prove the L∞ bound on ∇u for our equation (1.1), extending the result by DiBenedetto and Friedman to this more degenerate setting. We refer to [11] for an approach to this operator, based on viscosity techniques
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