Strong Unique Continuation Results for Differential Inequalities

✍ Scribed by Rachid Regbaoui

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 296 KB
• Volume: 148
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1997.3102

✦ Synopsis

The main result of this paper is a strong uniqueness theorem for differential inequalities of the form |2u(x)| |V(x) u(x)|+ |W(x) {u(x)|, where V and W are radial functions in L nÂ2 loc (0) and L n loc (0) respectively, and 0 is a connected open subset of R n . Other results involving other spaces of potentials V and W are proved. Our method relies on sharp Carleman estimates.

1997 Academic Press Recently, Wolff [11] gave a positive answer to this question in an even more general form where the Laplace operator is replaced by a second order elliptic differential operator with Lipschitz coefficients. But the analogous problem about strong unique continuation seems to be different, even for inequalities of type (1.1). The best result (as far as we know!) is article no.