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Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 6
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Articles

A remark on forward–backward parabolic equations

Pages 1042-1051 | Received 20 Oct 2017, Accepted 13 Nov 2017, Published online: 11 Dec 2017
 

ABSTRACT

In this note we deal with a problem regarding forward–backward parabolic equations like r(x)ut-uxx=0 with r which changes sign. It is natural to have the continuity of the function tu2(x,t)r(x)dx. Here we show that, under very mild assumptions, one also gets the continuity of the function tu2(x,t)|r(x)|dx also in more general and abstract situations. This result turns out to be useful when dealing with De Giorgi classes for these type of equations.

AMS SUBJECT CLASSIFICATIONS:

Notes

No potential conflict of interest was reported by the author.

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