Sentence examples for continuation results from inspiring English sources

In this region, the usual existence, uniqueness and continuation results hold for the system.

Existence, uniqueness and continuation results for system (11) hold in this region.

The uniform Sobolev inequalities and unique continuation results for second-order elliptic equations with constant coefficients studied in [2].

At continuation, results of implementation for proposed algorithm on the number of video image sequences is presented specially under complicated condition on the MATLAB software environment.

Thus, all the solutions inside the region Ω will be considered, where uniqueness of the solutions, and the usual existence and continuation results are satisfied.

In this paper, we established a quantitative unique continuation results for a coupled heat equations, with the homogeneous Dirichlet boundary condition, on a bounded convex domain Ω of (mathbb{R}^{d}) with smooth boundary ∂Ω.

We prove a strong unique continuation result for Schrödinger inequalities, i.e., we obtain that a flat u so that |Δu| ≤|Vu| should be zero, provided that V is a radial Kato potential.

We also establish the analogue of this unique continuation result in the case of non-periodic solutions defined on the whole real line with vanishing boundary conditions at infinity.

As a consequence, we can prove a unique continuation result in the style of the Hardy uncertainty principle, which generalizes the analogous theorems which have been recently proved by Escauriaza, Kenig, Ponce and Vega.

As for application, a continuation result is given.

The following corollary may be viewed as an abstract unique continuation result.