The phrase "above boundary" is correct and usable in written English.
It can be used in contexts where you are referring to a limit or threshold that is higher than a specified point or level.
Example: "The data collected from the experiment exceeded the above boundary, indicating a significant anomaly."
Alternatives: "upper limit" or "higher threshold".
criterion appears to be very accurate for the above boundary conditions.
Most studies have attempted to reconstruct an unknown spacewise-dependent source F x) from the final observation uT x):= u x,T), but from an engineering viewpoint, the above boundary data measurements are feasible.
Then, we extend the fine regularity theory for weak solutions of the elliptic equations with the above boundary conditions, known for bounded Lipschitz domains, to bounded W1,p-extension domains whose boundaries are upper d-sets, by showing that such weak solutions are globally Hölder continuous.
We prove that the realization of the p-Laplace operator with both of the above boundary conditions generate (nonlinear) ultracontractive submarkovian C0-semigroups on L2 Ω,dx)×L2(∂Ω,dμ), and hence, their associated first order Cauchy problems are both well posed on Lq Ω,dx)×Lq(∂Ω,dμ) for all measurable function q with 1⩽q⁎⩽q⁎<∞.
By Theorem 4.3, each of the above boundary value problems have eigenvalues.
We now evaluate y at the boundaries to show that the above boundary conditions are satisfied.
In the above faceted boundary, elastic strain energy induced by atomic mismatch across the boundary creates barriers to facet coarsening.
Both parties will respect and comply with the above international boundary.
The results of the analyses in terms of structural displacements and drifts for the above mentioned boundary conditions have been compared and discussed.
By Theorem 4.2, we know that the above transformed boundary value problems in each have eigenvalues.
Then, the structural motion equation of planar elastic tube bundle is calculated based on the above force boundary.
