Sharp regularity for the inhomogeneous porous medium equation (Preprint)

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Type: Preprint
National /International: International
Title: Sharp regularity for the inhomogeneous porous medium equation
Publication Date: 2017-06-14
Authors: - Damião J. Araújo
- Anderson F. Maia
- José Miguel Urbano
Abstract: We show that locally bounded solutions of the inhomogeneous porous medium equation

ut div(mum−1∇u) = f ∈ Lq,r, m > 1,

are locally Hölder continuous, with exponent

γ =min0/m , [(2q − n)r − 2q]/q[(mr − (m − 1)]},

where α0 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.
Institution: DMUC 17-31
Online version: http://www.mat.uc.pt...prints/eng_2017.html
Download: Not available
 
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