Indefinite fractional elliptic problem and Liouville theorems

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• 作者：Wenxiong Chen^a ; ^b ; ¹ ; ^{wchen@yu.edu" class="auth_mail" title="E-mail the corresponding author} ; Jiuyi Zhu^c ; ² ; ^{jzhu43@math.jhu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35B53 ; 35B45 ; 35B44 ; 35J70
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 March 2016
• 年：2016
• 卷：260
• 期：5
• 页码：4758-4785
• 全文大小：347 K

文摘

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