Pascal Bégout, and Fernando Soria, “A generalized interpolation inequality and its application to the stabilization of damped equations”, Communication in Partial Differential Equations, vol. 240, n. 2, September 2007, pp. 324–356.
In this paper, we establish a generalized Hölder's or interpolation inequality for weighted spaces in which the weights are non-necessarily homogeneous. We apply it to the stabilization of some damped wave-like evolution equations. This allows obtaining explicit decay rates for smooth solutions for more general classes of damping operators. In particular, for 1−d models, we can give an explicit decay estimate for pointwise damping mechanisms supported on any strategic point.