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title
lim Practice= Perfect
description
when time goes to infinity
site name
lim Practice= Perfect
author
updated
2026-02-25 01:04:12
raw text
lim Practice= Perfect | when time goes to infinity lim Practice= Perfect when time goes to infinity Classical interior estimate of harmonic functions by maximum principle Lemma 1 Suppose and on . Then Proof: Define where is a constant and is a cut-off function in such that on and . We want to show that takes its maximum only at the boundary . If this is true then Now let us assume takes a local maximum at some interior point . Then we must have the following at this point Using Young’t inequality for the cross term Inserting this to the previous inequality yields Taking large enough, one obtains a contradiction. Thus must take its maximum on the boundary. Remark: I see this proof from a talk given by Ben Weinkove in Beijing Normal University 2024. June 19, 2024 – 11:45 pm Categories: Elliptic PDE , PDE | Post a comment Tagged harmonic functions , maximum principle | Reflection in R2 Suppose we have two d...
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