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math.AP2012★ 14 cited
A Generalized Interpolation Inequality and its Application to the Stabilization of Damped Equations
Pascal Bégout, Soria Fernando
In this paper, we establish a generalized H{ö}lder's or interpolation inequality for weighted spaces in which the weights are non-necessarily homogeneous. We apply it to the stabil…
math.AP2012★ 3 cited
Regularity of solutions of the fractional porous medium flow
Luis Caffarelli, Fernando Soria, Juan Luis Vazquez
We study a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. More precisely, $$ u_t=\nabla\cdot(u\nabla (-Δ)^{-s}u), \quad \…