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Liouville’s theorem and the restricted biharmonic mean value property on the plane

Теорема Лиувилля и свойство ограниченности би-гармонического среднего на плоскости

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Abstract

In [3, 4], under some conditions we proved that a bounded Lebesgue measurable function satisfying the restricted biharmonic mean value property in ℝn, where n ≥ 3 or n = 1, is constant. In the present paper, we study the case n = 2.

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В работах [3, 4] при некоторых дополнительных условиях было установлено, что ограниченная иэмеримая по Лебегу функция, которая удовлетворяет условию ограниченности би-гармонического среднего в ℝn для n ≥ 3 и для n = 1 является постоянной. В настоящей работе мы исследуем случай n = 2.

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Authors and Affiliations

  1. Faculté des Sciences, Université Mohammed V-Agdal, Faculté des Sciences, B.P. 1014, Rabat, Morocco

    Mohamed El Kadiri

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  1. Mohamed El Kadiri
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Correspondence to Mohamed El Kadiri.

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El Kadiri, M. Liouville’s theorem and the restricted biharmonic mean value property on the plane. Anal Math 39, 209–216 (2013). https://doi.org/10.1007/s10476-013-0304-y

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  • DOI: https://doi.org/10.1007/s10476-013-0304-y

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