Journal article
FUNDAMENTAL SOLUTIONS OF A CLASS OF HOMOGENEOUS INTEGRO-DIFFERENTIAL ELLIPTIC EQUATIONS
Discrete and continuous dynamical systems, Vol.39(3), pp.1237-1256
03/01/2019
DOI: 10.3934/dcds.2019053
Abstract
In this paper, we study a class of integro-differential elliptic operators L-sigma with kernel k(y) = a(y)/vertical bar y vertical bar(d+sigma), where d >= 2, sigma is an element of (0, 2), and the positive function a(y) is homogenous and bounded. By using a purely analytic method, we construct the fundamental solution Phi of L-sigma if a(y) satisfies a natural cancellation assumption and vertical bar a(y) - 1 vertical bar is small. Furthermore, we show that the fundamental solution Phi is -alpha* homogeneous and Lipschitz continuous, where the constant alpha* is an element of (0, d). A Liouville-type theorem demonstrates that the fundamental solution Phi is the unique nontrivial solution of L-sigma u = 0 in R-d\{0} that is bounded from below.
Details
- Title: Subtitle
- FUNDAMENTAL SOLUTIONS OF A CLASS OF HOMOGENEOUS INTEGRO-DIFFERENTIAL ELLIPTIC EQUATIONS
- Creators
- Yi Cao - Shaanxi Normal UniversityJianhua Wu - Shaanxi Normal UniversityLihe Wang - Shanghai Jiao Tong University
- Resource Type
- Journal article
- Publication Details
- Discrete and continuous dynamical systems, Vol.39(3), pp.1237-1256
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- DOI
- 10.3934/dcds.2019053
- ISSN
- 1078-0947
- eISSN
- 1553-5231
- Number of pages
- 20
- Grant note
- 11126201; 11671243 / NSFC
- Language
- English
- Date published
- 03/01/2019
- Academic Unit
- Mathematics
- Record Identifier
- 9984240770902771
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