A NOTE ON WEIGHTED SOBOLEV SPACES RELATED TO WEAKLY AND STRONGLY DEGENERATE DIFFERENTIAL OPERATORS

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

Анотація


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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Посилання


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

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