Peter I. Kogut, Olha P. Kupenko, Guenter Leugering, Yue Wang


In this paper we discuss some issues related to Poincar´e’s inequality for a
special class of weighted Sobolev spaces. A common feature of these spaces is that they can be naturally associated with differential operators with variable diffusion coefficients that are not uniformly elliptic. We give a classification of these spaces in the 1-D case bases on a measure of degeneracy of the corresponding weight coefficient and study their key properties.

Ключові слова

Degenerate equation; weighted Sobolev spaces; Poincar´e’s inequality

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DOI: http://dx.doi.org/10.15421/141905


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Адреса редколегії: 49050, Україна, Дніпровський національний університет імені Олеся Гончара, вул. Козакова 18, корп. 14, механіко-математичний факультет, д-р фіз.-мат. наук, проф. Когут П.І. 

email: p.kogut@i.ua


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