Indefinite fractional elliptic problem and Liouville theorems

By Wenxiong CHEN *, Jiuyi Zhu. 2014

140 citations recorded by the source corpus.

In this paper, we consider the indefinite fractional elliptic problem. A corresponding Liouville-type theorem for the indefinite fractional elliptic equations is established. Furthermore, we obtain a priori bound for solutions in a bounded domain by blowing-up and re-scaling. We also classify the solutions of some degenerate elliptic equation originated from fractional Laplacian.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/3cccb6924c560ae01fa1d8c7cd5dada68100cf2c

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In Applied Mathematics

1. Tianling Jin
2. Wenxiong CHEN *
3. Jingang Xiong
4. Congming LI #
5. Yan Li
6. Yanyan Li
7. Guanfeng Li
8. Yahui Niu

In Computational Theory and Mathematics

1. Wenxiong CHEN *
2. Congming LI #
3. Jingang Xiong
4. Tianling Jin
5. Yan Li
6. Yanyan Li
7. Guanfeng Li
8. Yahui Niu

Citations in the corpus

• Asymptotic method of moving planes for fractional parabolic equations (2020, background): “During the last decade, elliptic nonlocal equations, especially those involving fractional Laplacians, have been studied by more and more scholars and a series of results have been obtained, such as [9] for symmetry and nonexistence of solutions, [12, 16] for Liouville Theorems with indefinite nonli”
• The Nirenberg problem and its generalizations: a unified approach (2014, background): “[10]; some Liouville theorem for indefinite fractional problem by Chen and Zhu [23]; etc.”
• A direct method of moving planes for the fractional Laplacian (2014, methodology): “This extension method has been applied successfully to study equations involving the fractional Laplacian, and a series of fruitful results have been obtained (see [BCPS] [CZ] and the references therein).”
• Maximum principles for a fully nonlinear fractional order equation and symmetry of solutions (2016, methodology): “This method has been applied successfully to study equations involving the fractional Laplacian, and a series of fruitful results have been obtained (see [1,11] and the references therein).”