Sentence examples for different regularity from inspiring English sources
Complex geometrical optics for first order equations and systems under different regularity assumptions of the coefficients have been constructed in [142, 144, 162, 163, 197].
In this paper we determine the multifractal nature of almost every function (in the prevalence setting) in a given Sobolev or Besov space according to different regularity exponents.
Whereas this lemma could be applied under different regularity assumptions on the domain, here we use it to estimate the spectrum in Lipschitz and in so-called Reifenberg-flat domains.
In order to apply this theory to understand the responses and bifurcation patterns of forced systems, it is fundamental to determine the regions in parameter space where the different regularity properties (e.g., continuity and injectivity) of the firing maps are satisfied.
Existence results of (L^p -valued soL^p -valuedlinear transolutionsblems under different regularity assumptiofs and various estimates needed linearare collectransportct. 4. They are then used in the Euler comproblems method in Sect. 5 to provide proofs of the theorems stated in Sect.
There have been many results about the first expansion of large solution for problem (1.1) with (p=2) and (b(x)), (f u)) satisfying some proper conditions under different regularity boundary conditions (see [21 28]) and the second expansion (see[29 34] and references therein).
In general, different readers may find different regularities controversial.
Thus, it makes sense to generate different models based on different regularities.
It was found that KLa and Dz change with different regularities in these different flow regimes.
This result was replicated using different stimuli and different regularities, suggesting that mixing consistent and random conditions leads to an overall slowing down of performance.
Additionally, the effect of relative density is analyzed for different regularities and results are compared with available analytical and semi-empirical models.
