where Ã¡n, denotes differentiation in the direction of tlie normal to 8B . As is well known, there are explicit formulas for the solutions of the aboye problems, and one can then give a very carefulâ€¦ (More)

âˆž(i.e. the solution scatters in á¸¢(R )). See section 2 of this paper for a review of these results. In the defocusing case, Bourgain ([5], [6]) proved that, for N = 3, 4 and u0 radial, this also holdsâ€¦ (More)

u(x, 0) = u0(x), where u0 âˆˆ H(R). Our principal aim here is to lower the best index s for which one has local well posedness in H(R), i.e. existence, uniqueness, persistence and continuous dependenceâ€¦ (More)

In this paper we improve an earlier result by Bukhgeim and Uhlmann [1], by showing that in dimension n â‰¥ 3, the knowledge of the Cauchy data for the SchrÃ¶dinger equation measured on possibly veryâ€¦ (More)

We prove that a potential q can be reconstructed from the Dirichlet-to-Neumann map for the SchrÃ¶dinger operator âˆ’âˆ†g + q in a fixed admissible 3-dimensional Riemannian manifold (M, g). We also showâ€¦ (More)

We study the initial value problem (IVP) associated to some canonical dispersive equations. Our main concern is to establish the minimal regularity property required in the data which guarantees theâ€¦ (More)

We prove that the Benjaminâ€“Ono initial value problem is globally well-posed in the Banach spaces H r (R), Ïƒ â‰¥ 0, of real-valued Sobolev functions.

Au â€” 0 in D; u = Æ’ on bD9 where Æ’ and its gradient on 3D belong to L(do). For C domains, these estimates were obtained by A. P. CalderÃ³n et al. [1]. For dimension 2, see (d) below. In [4] and [5] weâ€¦ (More)