INITIAL-BOUNDARY VALUE-PROBLEMS FOR PARABOLIC EQUATIONS IN LIPSCHITZ CYLINDERS

The initial-Dirichlet and initial-Neumann problems in Lipschitz cylinders are studied for the general second order parabolic equations of constant coefficients with squarely integrable boundary data. By layer potential method developed in the past decade, the author proves that the double layer potential and the single layer potential operators are invertible and hence obtains the solvability of the initial boundary value problems. Also, the solutions can be represented by these operators.