Sentence examples for to establish regularity from inspiring English sources

The aim of this paper is to establish regularity for weak solutions to the nondiagonal quasilinear degenerate elliptic systems related to Hörmander's vector fields, where the coefficients are bounded with vanishing mean oscillation.

The flexibility of these classes allows us to also establish regularity of solutions to rather general nonlinear integral equations.

We also establish regularity and positivity of the groundstates and prove that all positive groundstates are radially symmetric and monotone decaying about some point.

Later, in [3] Zhou and Fan studied the Cauchy problem of certain Boussinesq-α equations in n dimensions with n = 2 or 3. We establish regularity for the solution under ∇ u ∈ L 1 ( 0, T ; Ḃ ∞, ∞ 0 ).

Then the goal is to establish partial regularity theory.

The goal, then, is to establish partial regularity theory.

The aim of this paper is to establish a regularity criterion for it.

In this context, we use an A-harmonic approximation method to establish boundary regularity results.

we also give a result which helps to establish the regularity of a solution.

In addition, one may use a BSDE approach to establish the regularity property of a market model at hand.

Then the goal is to establish partial regularity of weak solutions for systems; see monographs [4 6] for more details.