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

Marius Ghergu, Vitali Liskevich, Zeev Sobol Orcid Logo

Journal d'Analyse Mathématique, Volume: 123, Issue: 1, Pages: 251 - 279

Swansea University Author: Zeev Sobol Orcid Logo

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DOI (Published version): 10.1007/s11854-014-0020-y

Abstract

We study the existence and nonexistence of positive singular solutions to second-order non-divergence type elliptic inequalities with measurable coefficients. We prove the existence of a critical value $p^*$ that separates the existence region from non-existence. In the critical case $p=p^*$ we show...

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Published in: Journal d'Analyse Mathématique
ISSN: 0021-7670 1565-8538
Published: 2014
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URI: https://cronfa.swan.ac.uk/Record/cronfa14656
first_indexed 2013-07-23T12:12:36Z
last_indexed 2018-02-09T04:46:09Z
id cronfa14656
recordtype SURis
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spelling 2017-12-18T16:11:01.5966266 v2 14656 2013-04-23 Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls f318e4c186ab19e3d3d3591a2e075d03 0000-0003-4862-427X Zeev Sobol Zeev Sobol true false 2013-04-23 MACS We study the existence and nonexistence of positive singular solutions to second-order non-divergence type elliptic inequalities with measurable coefficients. We prove the existence of a critical value $p^*$ that separates the existence region from non-existence. In the critical case $p=p^*$ we show that the existence of a singular solution depends on the rate at which the coefficients stabilize at zero and we provide some optimal conditions in this setting. Journal Article Journal d'Analyse Mathématique 123 1 251 279 0021-7670 1565-8538 31 12 2014 2014-12-31 10.1007/s11854-014-0020-y arXiv:1202.3426 arXiv:1209.1232 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2017-12-18T16:11:01.5966266 2013-04-23T12:38:57.4348581 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Marius Ghergu 1 Vitali Liskevich 2 Zeev Sobol 0000-0003-4862-427X 3
title Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls
spellingShingle Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls
Zeev Sobol
title_short Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls
title_full Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls
title_fullStr Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls
title_full_unstemmed Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls
title_sort Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls
author_id_str_mv f318e4c186ab19e3d3d3591a2e075d03
author_id_fullname_str_mv f318e4c186ab19e3d3d3591a2e075d03_***_Zeev Sobol
author Zeev Sobol
author2 Marius Ghergu
Vitali Liskevich
Zeev Sobol
format Journal article
container_title Journal d'Analyse Mathématique
container_volume 123
container_issue 1
container_start_page 251
publishDate 2014
institution Swansea University
issn 0021-7670
1565-8538
doi_str_mv 10.1007/s11854-014-0020-y
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url arXiv:1202.3426
document_store_str 0
active_str 0
description We study the existence and nonexistence of positive singular solutions to second-order non-divergence type elliptic inequalities with measurable coefficients. We prove the existence of a critical value $p^*$ that separates the existence region from non-existence. In the critical case $p=p^*$ we show that the existence of a singular solution depends on the rate at which the coefficients stabilize at zero and we provide some optimal conditions in this setting.
published_date 2014-12-31T10:46:53Z
_version_ 1850664931982049280
score 11.088971

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