Backward estimates for nonnegative solutions to a class of singular parabolic equations

摘要

In this paper we improve a recent result of the same Authors (Recalde and Vespri, 2015) by using the same approach in a more tricky way. More precisely, we study a class of quasilinear singular parabolic equations with L-infinity coefficients, whose prototypes are the p-Laplacian (2N/N+1 < p < 2) equations. Let us consider nonnegative solutions defined in R+ x R-N. We recall that in Recalde and Vespri (2015), starting from the value attained in a point (x(0), t(0)) by the solution, we proved sharp estimates in the stripe ((1 - epsilon) t(0),infinity) x R-N. In this note we show that, quite surprisingly, sharp estimates hold also for the remote past i.e. also for the stripe (0, t(0)) x R-N.