Layer potentials for elliptic operators with DMO-type coefficients: big pieces $Tb$ theorem, quantitative rectifiability, and free boundary problems

Andrea Merlo, Mihalis Mourgoglou, Carmelo Puliatti

For $n\ge 2$, we consider the operator $L_A=-\mathrm{div}(A(\cdot )\nabla )$, where $A$ is a uniformly elliptic $(n+1)\times (n+1)$ matrix with variable coefficients, a Radon mea…