Sentence examples for method of continuity from inspiring English sources

The solvability then follows from (2.5), the Poincaré inequality, and the method of continuity.

The existence and regularity of the unique solution w can be proved by applying classical methods, for instance, the method of continuity (see [29]).

Thus, taking into account the result of Lemma 5.1 and using the method of continuity along a parameter (see, e.g., Theorem 5.2 of [26]), we obtain the claimed result.

Therefore, this latter result and estimate (5.13) allow to use the method of continuity along a parameter in order to prove that the problem (5.15). is likewise uniquely solvable.

From the estimates (2.1),(2.2), Theorem 1.1 follows immediately by using Theorem 2.1, (instead of Theorem 1.1 in [20]), in the method of continuity argument presented in Section 5 of [20].

An approach, based upon the Method of Continuity, is presented for the numerical solution of n simultaneous non-linear equations in m variables (m ⪢ n) where any combination of n variables may be considered unknown.

For the critical case (alpha=1), by the method of modulus of continuity [10] and the Fourier localization technique, Yuan and Yuan [11] proved the global well-posedness in the critical Besov space (dot{B}_{p,1}^{frac{3}{p}}(mathbb{R}^{3})), (1leq p leqinfty).

Based on Besov space techniques and the method of modulus of continuity, Yamazaki [12] studied the regularized IPM equation in the supercritical regime and the global well-posedness was established in the Sobolev space (H^{m}(mathbb{R}^{3})), (m inmathbb {Z}^), (m>frac{5}{2}).

In conclusion, the use of this method enabled continuity of design language of the location; furthermore it was observed that information usage fields of students towards location and society have increased in number.

It is therefore important to develop reliable methods of measuring continuity that take account of the way complex care is delivered.

Among these methods, a variety of continuity or Brezis-type monotonicity conditions of f are commonly necessary.