## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

DCDS

Starting from the partial regularity results for suitable weak solutions to the Navier-Stokes Cauchy problem by Caffarelli, Kohn and Nirenberg [

DCDS-S

We are interested in regularity results, up to the boundary, for the
second derivatives of the solutions of some nonlinear systems
of partial differential equations with
$p$-growth. We choose two representative cases: the ''full gradient
case'', corresponding to a $p$-Laplacian, and the ''symmetric
gradient case'', arising from
mathematical physics. The domain is either the ''cubic domain''
or a bounded open subset of $\mathbb{R}^3$ with a smooth boundary. Depending
on the model and on the range of $p$, $p<2$ or $p>2$, we prove
different regularity results. It is worth noting that in the full
gradient case with $p<2$ we cover the singular case and obtain
$W^{2,q}$-global regularity results, for arbitrarily large values of
$q$. In turn, the regularity achieved implies the Hölder
continuity of the gradient of the solution.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]