L. Escauriaza et Jk. Seo, REGULARITY PROPERTIES OF SOLUTIONS TO TRANSMISSION PROBLEMS, Transactions of the American Mathematical Society, 338(1), 1993, pp. 405-430
We show that the gradients of solutions to certain elliptic and parabo
lic transmission problems with internal Lipschitz boundary and constan
t coefficients at each side of the internal boundary are square integr
able along the internal boundary.