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The weighted reverse poincaré type inequality for the difference of two parabolic subsolutions

  • Muhammad Shoaib Saleem , Kakha Shashiashvili and Malkhaz Shashiashvili EMAIL logo
Published/Copyright: November 3, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 4

Abstract

A new type weighted reverse Poincaré inequality is established for a difference of two continuous weak parabolic subsolutions of a linear second order uniformly parabolic partial differential equation with constant coefficients in the cylindrical domain.

This inequality asserts that if two continuous weak parabolic subsolutions are close in the uniform norm, then their gradients are close in the weighted L2 norm.

Keywords: weak parabolic subsolutions; reverse Poincaré inequality; gradient of the subsolution
MSC 2010: Primary 35K10; 35D30

(Communicated by Andras Ronto)

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Received: 2012-11-14
Accepted: 2014-3-10
Published Online: 2016-11-3
Published in Print: 2016-8-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0192
Keywords for this article
weak parabolic subsolutions; reverse Poincaré inequality; gradient of the subsolution

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