Sentence examples for a result of regularity from inspiring English sources

Then, in order to have a weaker hypothesis on f, we prove a result of regularity for the composition of the Nemytskii operator with a Stepanov-like weighted pseudo almost periodic function, assuming a compactness condition.

end{aligned} (1.3) We assume (tilde{Q}, tilde{phi}in C^{infty}(partialOmega)), thus we have (tilde{Q}_{0}, tilde{phi}_{0}in C^{infty}(bar{ Omega})) by standard results of regularity.

Let T be a subspace in X 2. The set Γ ( T ) : = { λ ∈ C :  there exists  c > 0  such that ∥ f − λ x ∥ ≥ c ∥ x ∥  for all  ( x, f ) ∈ T }. is called to be the regularity field of T. First, we give a result for the regularity field of Γ ( H 0 . Lemma 7.1 Assume that a is finite.

Additionally, we present a result concerning the regularity of the effective diffusivity tensor with respect to the parameters related to the statistics of the drift.

We also exhibit a result on microlocal regularity for solutions of first order partial differential equations in these classes, that do not seem possible to prove using the classical FBI transform.

The proof relies on a result on maximal regularity under the assumption of suitable off-diagonal bounds due to S. Blunck and the author, which we improve here.

As a result, the underlying regularities of the data can be captured, leading to better performance, e.g., in recognition [23].

The challenges are particularly accentuated for hyperbolic and convection-dominated PDEs as the discontinuities in physical space such as shocks can propagate into stochastic space resulting in a loss of regularity of the underlying solution with respect to the random parameters.

Now we give a regularity result of an ( l, m ) weak solution.

9 we then gather a series of regularity results that follow as a corollary of the theory presented.

The qualitative and quantitative results are consistent in showing differences in daily travel time budgets according to the day of the week, resulting in a degree of regularity and a weekly cycle (commonly inferred from cross-sectional data).