Isolated singularities of positive solutions of elliptic equations with weighted gradient term

NGUYEN, Phuoc-Tai. Isolated singularities of positive solutions of elliptic equations with weighted gradient term. Analysis & PDE. United States: Mathematical Sciences Publishers, 2016, vol. 9, No 7, p. 1671-1692. ISSN 2157-5045. Available from: https://dx.doi.org/10.2140/apde.2016.9.1671.

Basic information

• Original name: Isolated singularities of positive solutions of elliptic equations with weighted gradient term
• Authors: NGUYEN, Phuoc-Tai (704 Viet Nam, guarantor, belonging to the institution).
• Edition: Analysis & PDE, United States, Mathematical Sciences Publishers, 2016, 2157-5045.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: United States of America
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• RIV identification code: RIV/00216224:14310/16:00104019
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.2140/apde.2016.9.1671
• UT WoS: 000389831800004
• Keywords in English: gradient terms;weak singularities;strong singularities;removability
• Tags: International impact, Reviewed

Abstract

Let $\Omega \subset \mathbb{R}^N$ ($N>2$) be a $C^2$ bounded domain containing the origin $0$. We study the behavior near $0$ of positive solutions of equation (E) $-\Delta u + |x|^\alpha u^p + |x|^\beta |\nabla u|^q= 0$ in $\Omega \setminus \{0\}$ where $\alpha>-2$, $\beta>-1$, $p>1$ and $q>1$. When $1