For harmonic symbols we find the regularity required of the symbol for the formula to hold.
Depending on the precise situation and on the regularity required of the solution, boundary conditions at just one or both endpoints of the free surface need to be imposed.
As has been pointed out before, the functionals Φ, Ψ satisfy the assumptions of regularity required in Lemma 2.4.
This reconnects the theory presented here to the classical Calderón Zygmund theory, where VMO-regularity of coefficients is required to establish integrability estimates related to estimate (32); see for instance [9].
The purpose (as yet to be fully tested) is to eliminate the time consuming and repetitive regularity with which ministries are required to prepare, ab initio, complex documentation to meet the distinct requirements of each individual putative health sector donor.
The most vivid image of the marriage is of her cutting her husband's corns, a task she seems required to perform with dreadful regularity.
In order to obtain a better forecasting result, more information about the load system is required to explore the internal regularity of the fluctuating system load.
In general, graphs are not required to have any type of regularity.
Regularities require explanations, and to be natural these explanations must come from the natures of the creatures.
The quality of such models can be improved in a beautification step, where geometric regularities need to be detected and imposed on the model, and defects requiring topological change need to be corrected.
(2.54) We note that the regularity properties of (c x,t)) in (2.45) ensure that (varphi x,t)) has the regularity properties required in (2.6).
