We consider non-negative, weak solutions to the doubly nonlinear parabolic equation \[ \partial_t (u^q) − div(|Du|^{p−2}Du) = 0 \] in the super-critical fast diffusion regime 0 < p− 1 < q < N(p − 1)/(N − p)_+. We show that when solutions vanish continuously at the Lipschitz boundary of a parabolic cylinder Ω_T , they satisfy proper Carleson estimates. Assuming further regularity for the boundary of the domain Ω_T , we obtain a power-like decay at the boundary and a boundary Harnack inequality.
Boundary Estimates for Doubly Nonlinear Parabolic Equations
Ugo Gianazza;
2025-01-01
Abstract
We consider non-negative, weak solutions to the doubly nonlinear parabolic equation \[ \partial_t (u^q) − div(|Du|^{p−2}Du) = 0 \] in the super-critical fast diffusion regime 0 < p− 1 < q < N(p − 1)/(N − p)_+. We show that when solutions vanish continuously at the Lipschitz boundary of a parabolic cylinder Ω_T , they satisfy proper Carleson estimates. Assuming further regularity for the boundary of the domain Ω_T , we obtain a power-like decay at the boundary and a boundary Harnack inequality.File in questo prodotto:
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