Carleman estimates and unique continuation for second-order elliptic equations with nonsmooth coefficients

In this work we obtain strong unique continuation results for variable coefficient second order parabolic equations. The coefficients in the principal part are assumed to satisfy a Lipschitz condition in x and a Hölder C 1 3 condition in time. The coefficients in the lower order terms, i.e. the potential and the gradient potential, are allowed to be unbounded and required only to satisfy mixed norm bounds in scale invariant L p t Lq x spaces. 1.