Sentence examples for singular set of solutions from inspiring English sources

Further more, the dimension of singular set of solutions to non-differentiable elliptic systems are reduced by Kristensen and Mingione [9, 10].

Corollary 1.1 Under the assumptions of Theorem  1.1, the singular set of the weak solution u has ( n − m ) -dimensional Hausdorff measure zero in Ω ¯.

Under the assumptions of Theorem 1.1, the singular set of the weak solution u has (n − 2 -dimensional Hausdorff measure zero in Ω ̄.

As an immediately corollary we can derive an estimates of Hausdorff dimension on the possible singular set of a suitable weak solution as in the case of pure fluid.

Note again that the geodesic avoids the singular set of the surface.

More pragmatically, given its organic nature, the movement has no defined leadership, and no singular set of demands.

The author does not offer a sweeping set of solutions.

Propose a solution or a set of solutions.

We study Hausdorff dimension of boundary singular set for suitable weak solutions of the incompressible Navier Stokes equations.

We consider suitably weak solutions (u, p) to the incompressible Navier Stokes equations and under various assumptions on u obtain estimates for the size of its singular set.

We understand the global structure of the singular set through a Hopf-type index theorem.