Sentence examples for continuity of the weak from inspiring English sources

The space-time Hölder continuity of the weak solution is also discussed as a byproduct.

Note that the discontinuous coefficient is not so crucial for Hölder continuity of the weak solutions to the scalar partial differential equations, which is due to the famous De Giorgi-Moser-Nash iterative technique; see [1].

In [2 4], Campanato obtained the (L^{2,lambda } -regularity and Hölder continuity for the weak solutions of elliptic systems with continuous coefficients.

Next, a Petrov-Galerkin approach with shape and weighting functions matching all differentiability and continuity requirements of the weak formulation is applied to solve the consequent partial differential equation.

Note that a continuous and affine map is weakly continuous, so the weak continuity of is not required as well.

As stressed in [5], in many applications, it is always not possible to show the weak continuity of the involved mappings, while the sequential weak continuity offers no problem.

The method of analysis taking into account the shear effect or the continuity of the granular piles-weak soil composite and the nonlinear behavior of weak soil and granular piles.

Using compactness of the class S and continuity of the eigenvalues in the weak topologies, problem (1.4) can be realized by some optimal weight w.

We point out that in the main results of [3, 24], the condition of the sequentially continuity from the weak topology to the strong topology for the derivative K' of the function K : C → ℝ is very strong.

We remark that Lemma 2.6 is not a consequence of Lemma 3.1 in [5], because the condition of the sequential continuity from the weak topology to the strong topology for the derivative of the function does not cover the case.

These springs connected at their ends by a thin membrane under uniform tension to overcome the drawbacks of Winkler model related to the shear effect or the continuity of the granular piles-weak soil composite.