Gradient type estimates for linear elliptic systems from composite materials
Abstract
In this paper, we consider linear elliptic systems from composite materials where the coefficients depend on the shape and might have the discontinuity between the subregions. We derive a function which is related to the gradient of the weak solutions and which is not only locally piecewise H\"{o}lder continuous but locally H\"{o}lder continuous. The gradient of the weak solutions can be estimated by this derived function and we also prove local piecewise gradient H\"{o}lder continuity which was obtained by the previous results.
Cite
@article{arxiv.2206.07880,
title = {Gradient type estimates for linear elliptic systems from composite materials},
author = {Youchan Kim and Pilsoo Shin},
journal= {arXiv preprint arXiv:2206.07880},
year = {2022}
}
Comments
The results of this paper was announced at 'International Conference on Partial Differential Equations Related to Material Science', May 6-9, 2021. One long paper is splitted into two papers 'Gradient type estimates for linear elliptic systems from composite materials' and 'Piecewise smoothness for linear elliptic systems with piecewise smooth coefficients'