Abstract
The Expansion of Positivity is a property of nonnegative supersolutions to elliptic and parabolic partial differential equations, that is at the heart of any form of Harnack estimate. Roughly speaking, it asserts that information on the measure of the “positivity set” of u at the time level s, over the cube K ρ(y), translates into an expansion of the positivity set both in space (from a cube K ρ(y) to K 2ρ(y)), and in time (from s to s + θρ 2, for some suitable θ).
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© 2012 Springer Science+Business Media, LLC
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DiBenedetto, E., Gianazza, U., Vespri, V. (2012). Expansion of Positivity. In: Harnack's Inequality for Degenerate and Singular Parabolic Equations. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1584-8_4
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DOI: https://doi.org/10.1007/978-1-4614-1584-8_4
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Print ISBN: 978-1-4614-1583-1
Online ISBN: 978-1-4614-1584-8
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