Journal
AMERICAN JOURNAL OF MATHEMATICS
Volume 145, Issue 1, Pages 151-219Publisher
JOHNS HOPKINS UNIV PRESS
DOI: 10.1353/ajm.2023.0003
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We prove optimal boundary regularity for bounded positive weak solutions of fast diffusion equations in smooth bounded domains, answering a problem raised by Berryman and Holland in 1980 for these equations in the subcritical and critical regimes. Our proof utilizes a geometric type structure of the fast diffusion equations, where an important component is an evolution equation for a curvature-like quantity.
We prove optimal boundary regularity for bounded positive weak solutions of fast diffusion equations in smooth bounded domains. This solves a problem raised by Berryman and Holland in 1980 for these equations in the subcritical and critical regimes. Our proof of the a priori estimates uses a geometric type structure of the fast diffusion equations, where an important ingredient is an evolution equation for a curvature-like quantity.
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