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  5. Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls
 
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Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls

Author(s)
Ghergu, Marius  
Liskevich, Vitali  
Sobol, Zeev  
Uri
http://hdl.handle.net/10197/6149
Date Issued
2014-07-24
Date Available
2015-07-24T03:00:17Z
Abstract
We study the existence and non-existence of positive singular solutions of second-order non-divergence type elliptic inequalities of the form $\sum\limits_{i,j = 1}^N {a_{ij} (x)\frac{{\partial ^2 u}} {{\partial x_i \partial x_j }}} + \sum\limits_{i = 1}^N {b_i (x)\frac{{\partial u}} {{\partial x_i }} \geqslant K(x)u^p ,} - \infty < p - \infty , $ with measurable coefficients in a punctured ball B R \{0} of ℝ N , N ≥ 1. We prove the existence of a critical value p* which separates the existence region from the non-existence region. We show that in the critical case p = p*, the existence of a singular solution depends on the rate at which the coefficients (a i j ) and (b i ) stabilize at zero, and we provide some optimal conditions in this setting.
Other Sponsorship
Royal Irish Academy
Romanian Ministry of Education, Research, Youth and Sport
Type of Material
Journal Article
Publisher
Springer
Journal
Journal D'Analyse Mathematique
Volume
123
Issue
1
Start Page
251
End Page
279
Subjects

Non-divergence semi-l...

Singular solutions

Punctured ball

Critical exponent

DOI
10.1007/s11854-014-0020-y
Language
English
Status of Item
Peer reviewed
This item is made available under a Creative Commons License
https://creativecommons.org/licenses/by-nc-nd/3.0/ie/
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paperGLS.pdf

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392.33 KB

Format

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Owning collection
Mathematics and Statistics Research Collection

Item descriptive metadata is released under a CC-0 (public domain) license: https://creativecommons.org/public-domain/cc0/.
All other content is subject to copyright.

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