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arXiv · 2006.03894

Sharp regularity for the inhomogeneous porous medium equation

Damião J. Araújo·Anderson F. Maia·José Miguel Urbano
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Abstract

We show that locally bounded solutions of the inhomogeneous porous medium equation $$u_{t} - {\rm div} \left( m |u|^{m-1} \nabla u \right) = f \in L^{q,r}, \quad m >1 ,$$ are locally Hölder continuous, with exponent $$γ=\min \left\{ \frac{α_{0}^-}{m}, \frac{[(2q - n)r -2q]}{q[(mr - (m-1)]} \right\},$$ where $α_{0}$ denotes the optimal Hölder exponent for solutions of the homogeneous case. The proof relies on an approximation lemma and geometric iteration in the appropriate intrinsic scaling.

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Damião J. Araújo, Anderson F. Maia, José Miguel Urbano. 2020-06-06. Sharp regularity for the inhomogeneous porous medium equation. https://doi.org/10.1007/s11854-020-0081-z

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