Journal article 1046 views
Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls
Journal d'Analyse Mathématique, Volume: 123, Issue: 1, Pages: 251 - 279
Swansea University Author:
Zeev Sobol
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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...
| Published in: | Journal d'Analyse Mathématique |
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| ISSN: | 0021-7670 1565-8538 |
| Published: |
2014
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa14656 |
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| 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 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. |
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| Item Description: |
arXiv:1209.1232 |
| College: |
Faculty of Science and Engineering |
| Issue: |
1 |
| Start Page: |
251 |
| End Page: |
279 |