We prove a strong unique continuation result for SchrΓΆdinger inequalities, i.e., we obtain that a flat \(u\) so that \(|\Delta u| \leqslant|V u|\) should be zero, provided that \(V\) is a radial Kato potential. It gives an extension of a result by E. B. Fabes, N. Garofalo and F. H. Lin [3] who got a
Strong Uniqueness for Second Order Differential Operators
β Scribed by Rachid Regbaoui
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 283 KB
- Volume
- 141
- Category
- Article
- ISSN
- 0022-0396
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
HILBERT space L,(D) where the coefficients always fulfil the following conditions. ## i) ii) a@), q(z) E Cl(l2) and real-valued, a&) = a@), x E D, ( 7) Denoting the domain of the FRIEDRICHS extension A by D(A) we have W ) r H A . 5 mR"). 1) W#W) is the completion of Com(Rn) in the norm Ilullw&BT8
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 nΓ2 loc (0) and L n loc (0) respectively, and 0 is a connected open subset of R n . Other results involving other spaces o
Left definite theory of regular self-adjoint operators in a Sobolev space was developed a rew years ago when the boundary conditions were separated, the separation being necessary in order to properly define the Sobolev inner product. We show how this may be extended when the boundary conditions are