A NOTE ON WEIGHTED SOBOLEV SPACES RELATED TO WEAKLY AND STRONGLY DEGENERATE DIFFERENTIAL OPERATORS
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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Oles Honchar Dnipro National University
2019-09-01
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| Series: | Journal of Optimization, Differential Equations and Their Applications |
| Subjects: | |
| Online Access: | https://model-dnu.dp.ua/index.php/SM/article/view/136 |
| Summary: | 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. |
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| ISSN: | 2617-0108 2663-6824 |