Sentence examples for continuity of solutions from inspiring English sources

Last, we prove the global Hölder continuity of solutions provided that their restrictions on boundary are Hölder continuous.

Conditions on Γ that will guarantee the existence, uniqueness, and continuity of solutions to the above equation are given.

The existence, uniqueness, boundness of solutions of the system and continuity of solutions with respect to the uncertain parameter appeared in the studied system are also discussed.

Opposite to the deterministic case where smooth initial conditions may develop discontinuities, we prove that a certain Sobolev degree of regularity is maintained, which implies Hölder continuity of solutions.

Especially, we show the Hölder continuity of solutions.

Existence, integrability, boundedness, and continuity of solutions to anisotropic elliptic equations have received much attention; see [7 15] and the references therein.

This allows us to define a good notion of integral with respect to irregular paths with Hölder exponent greater than 1/3 (e.g. samples of Brownian motion) and study the problem of the existence, uniqueness and continuity of solution of differential equations driven by such paths.

Step three: the continuity of solution with the initial data.

These assumptions are about continuity of solution space and differentiability of the objective function.

In Section 3, we investigate the existence, uniqueness, stability, and continuity of solution to the nonlinear equation (1.3).

Chen and Li [11] studied the continuity of solution sets for parametric generalized systems without the uniform compactness assumption, which improves the corresponding results in [8].