Sentence examples for optimal regularity from inspiring English sources

and the optimal regularity.

In particular, the optimal regularity result can be obtained.

In particular, we get the optimal regularity by the method of A-caloric approximation introduced by Duzaar and Mingione.

We obtain optimal regularity results in the natural family of Sobolev spaces associated with the variational structure of the equations.

The optimal regularity results are strongly related to an explicit exponent which is larger than the critical Sobolev exponent.

The goal of this section is to investigate the optimal regularity for solutions of (1) with f having a jump discontinuity in the t-variable.

Further, we establish the optimal partial regularity result of very weak solutions to (1.1).

In this article, we shown optimal boundary regularity of (1.1) under controllable growth condition.

Motivated by these works, we mainly consider the optimal partial regularity to nonhomogeneous A-harmonic systems in the form of (1.1) under assumptions (H1 - H4).

Inspired by this work, Yu and Zheng [33] obtained optimal partial regularity for quasilinear elliptic systems with VMO coefficients by a modification of A-harmonic approximation argument.

The focus is on obtaining optimal Hölder regularity of these solutions assuming fairly minimal conditions on the underlying metric and potential.