What is it about?
A new type weighted reverse Poincare inequality is established for a difference of two continuous weak parabolic sub solutions 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 sub solutions are close in the uniform norm, then their gradients are close in the weighted L2 norm.
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Why is it important?
This inequality asserts that if two continuous weak parabolic sub solutions are close in the uniform norm, then their gradients are close in the weighted L2 norm.
Perspectives
This inequality estimates the L2 weighted norm between gradients by the uniform norm between weak sub solutions
Professor Malkhaz Shashiashvili
Ivane Javakhishvili Tbilisi State University
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This page is a summary of: The weighted reverse poincaré type inequality for the difference of two parabolic subsolutions, Mathematica Slovaca, January 2016, De Gruyter,
DOI: 10.1515/ms-2015-0192.
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