Hardy-type inequalities and Pohozaev-type identities for a class of p-degenerate subelliptic operators and applications

✍ Scribed by Huiqing Zhang; Pengcheng Niu

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 201 KB
• Volume: 54
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(03)00062-2

✦ Synopsis

The purpose of this paper is to consider a class of p-degenerate subelliptic operators Lp constructed by generalizing Greiner's vector ÿelds. Their fundamental solutions at the origin are established with the aid of the properties of radial functions. A Picone-type identity and a Hardy-type inequality with respect to vector ÿelds are proved. Some Pohozaev-type identities and applications to nonlinear equations are given. Finally, a Carleman-type estimate and uniqueness of the operator L2 are discussed.