Elliptic systems with measurable coefficients of the type of Lamé system in three dimensions - Mathematics > Analysis of PDEs

Abstract: We study the $3 \times 3$ elliptic systems $abla \times ax abla\timesu- abla bx abla \cdot u=f$, where the coefficients $ax$ and $bx$are positive scalar functions that are measurable and bounded away from zeroand infinity. We prove that weak solutions of the above system are H\-oldercontinuous under some minimal conditions on the inhomogeneous term $f$. We alsopresent some applications and discuss several related topics includingestimates of the Green-s functions and the heat kernels of the above systems.

Author: Kyungkeun Kang, Seick Kim

Source: https://arxiv.org/