Poincaré-Type Inequalities for the Composite Operator in -Averaging Domains

Guannan Shi, Yuming Xing and Baiqing Sun

Abstract and Applied Analysis, 2014, vol. 2014, 1-7

Abstract:

We first establish the local Poincaré inequality with -averaging domains for the composition of the sharp maximal operator and potential operator, applied to the nonhomogenous -harmonic equation. Then, according to the definition of -averaging domains and relative properties, we demonstrate the global Poincaré inequality with -averaging domains. Finally, we give some illustrations for these theorems.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:675464

DOI: 10.1155/2014/675464

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