In this paper we prove strong unique continuation for u satisfying an inequality of the form |δmu| ≤ f(x, u,Du, ⋯ ,D ku), where k is up to [3m/2]. This result gives an improvement of a work by Colombini and Grammatico (1999) in some sense. The proof of the main theorem is based on Carleman estimates with three-parameter weights |x| 2σ1 (log |x|)2σ2 exp( β/2 (log |x|)2).
All Science Journal Classification (ASJC) codes
- Applied Mathematics