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

Files in This Item:
File Description SizeFormat 
paperGLS.pdf392.33 kBAdobe PDFDownload
Title: Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls
Authors: Ghergu, Marius
Liskevich, Vitali
Sobol, Zeev
Permanent link: http://hdl.handle.net/10197/6149
Date: 24-Jul-2014
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.
Type of material: Journal Article
Publisher: Springer
Keywords: Non-divergence semi-linear equation;Singular solutions;Punctured ball;Critical exponent
DOI: 10.1007/s11854-014-0020-y
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

Show full item record

SCOPUSTM   
Citations 50

6
Last Week
0
Last month
checked on Jun 22, 2018

Page view(s) 50

41
checked on May 25, 2018

Download(s) 50

19
checked on May 25, 2018

Google ScholarTM

Check

Altmetric


This item is available under the Attribution-NonCommercial-NoDerivs 3.0 Ireland. No item may be reproduced for commercial purposes. For other possible restrictions on use please refer to the publisher's URL where this is made available, or to notes contained in the item itself. Other terms may apply.