A NOTE on WEIGHTED SOBOLEV SPACES RELATED to WEAKLY and STRONGLY DEGENERATE DIFFERENTIAL OPERATORS

Kogut PI, Kupenko OP, Leugering G, Wang Y (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Journal of Optimization, Differential Equations and Their Applications Oles Honchar Dnipro National University

Book Volume: 27

Pages Range: 1-22

Journal Issue: 2

DOI: 10.15421/141905

Abstract

In this paper we discuss some issues related to Poincaré’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.

Authors with CRIS profile

Günter Leugering Lehrstuhl für Angewandte Mathematik Yue Wang Lehrstuhl für Angewandte Mathematik

Involved external institutions

Oles Honchar Dnipropetrovsk National University / Дніпропетровський національний університет імені Олеся Гончара UA Ukraine (UA) Dnipro Polytechnic National Technical University / Національний технічний університет UA Ukraine (UA)

How to cite

APA:

Kogut, P.I., Kupenko, O.P., Leugering, G., & Wang, Y. (2019). A NOTE on WEIGHTED SOBOLEV SPACES RELATED to WEAKLY and STRONGLY DEGENERATE DIFFERENTIAL OPERATORS. Journal of Optimization, Differential Equations and Their Applications, 27(2), 1-22. https://dx.doi.org/10.15421/141905

MLA:

Kogut, Peter I., et al. "A NOTE on WEIGHTED SOBOLEV SPACES RELATED to WEAKLY and STRONGLY DEGENERATE DIFFERENTIAL OPERATORS." Journal of Optimization, Differential Equations and Their Applications 27.2 (2019): 1-22.

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