  Common proofs of the Gagliardo-Nirenberg-Sobolev (GNS) do not provide
explicit bounds on the involved constants, unless a sharp constant is being
determined. GNS inequalities naturally occur in error estimates for numerical
approximations. In particular, bounds on GNS constants allow us to provide
explicit a priori estimates. We provide an algorithm that determines upper
bounds on the non-endpoint homogeneous GNS inequalities in terms of explicit
upper bounds for Young's convolution inequality and parabolic estimates. Our
method is based on the heat-kernel representation of the inverse Laplacian,
from which we deduce interpolation estimates.
