  The Gelfand-Yaglom formula relates functional determinants of the
one-dimensional second order differential operators to the solutions of the
corresponding initial value problem. In this work we generalise the
Gelfand-Yaglom method by considering discrete and continuum partial second
order differential operators in higher dimensions. To illustrate our main
result we apply the generalised formula to the two-dimensional massive and
massless discrete Laplace operators and calculate asymptotic expressions for
their determinants.
