Poincaré‐Type Inequalities for the Composite Operator in L𝒜‐Averaging Domains

Guannan Shi, Yuming Xing and Baiqing Sun

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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

Date: 2014
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https://doi.org/10.1155/2014/675464

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:675464

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