arXiv subjects

Liang Song

Publications and source records attributed to Liang Song.

74 records · Page 5Linked to original sources

arXiv2012

On Lp Estimates in Homogenization of Elliptic Equations of Maxwell's Type

For a family of second-order elliptic systems of Maxwell's type with rapidly oscillating periodic coefficients in a $C^{1, α}$ domain $Ω$, we establish uniform estimates of solutions $u_\varep$ and $\nabla \times u_\varep$ in $L^p(Ω)$ for $1<p\le \infty$. The proof relies on the uniform $W^{1,p}$ and Lipschitz estimates for solutions of scalar elliptic equations with periodic coefficients.

math.AP↗

arXiv2011

Uniform W^{1,p} Estimates for Systems of Linear Elasticity in a Periodic Medium

Let $\mathcal{L}_ε$ be a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients. We obtain the uniform $W^{1,p}$ estimate in a Lipschitz domain for solutions to the Dirichlet problem, where $(2n/(n+1)) -δ<p<(2n/(n-1))+δ$. The ranges of $p$'s are sharp for $n=2$ or 3.

math.AP↗