SOLA are special because they are selected via an approximation procedure using more regular energy solutions, and thereby they inherit a few of their basic properties.
In the three-dimensional case, a uniqueness result similar to the one for Navier-Stokes equations is given and the same result concerning fractional derivatives is obtained, but only for a more regular weak solution.
El Dika and Molinet proved the stability of multi-peakons [8] and multi-anti-peakons-peakons [9] among a slightly more regular class of solutions.
Chain or sequence folding is much more regular in the solution crystallized material, and amorphous layer thickness is reduced from about 8 nm to 3 nm.
Indeed, the proof of Lemma 31 is based essentially on Corollary 24 providing a function dominating the weak solution for "more regular" coefficients.
We ask the following question: (Q) Can the solution u be more regular that f?
Note here that the function f is just in (operatorname {AAU}(mathbb{R}times C,mathbb{R})), whereas the obtained solution x is more regular, namely, x is in (operatorname{KAA}(mathbb{R},mathbb{R})).
Addition of ethanol to the reaction solution results in much more regular ZnO slices in Fig. 3a than those in Fig. 3c.
Solutions for which structural considerations are dominant are called athermal solutions, and those for which the effects of intermolecular forces are more important than those of structure are called regular solutions (see below Regular and athermal solutions).
Regularization aims to make the problem less complex (more regular), i.e. to ensure the uniqueness of the solution [ 84], to reduce the ill-conditioning and to avoid model overfitting.
