Regularity and time behavior of the solutions of linear and quasilinear parabolic equations

01 Pubblicazione su rivista
Porzio M. M.
ISSN: 1079-9389

In this paper we study the regularity, the uniqueness and the asymptotic behavior of the solutions to a class of nonlinear operators in dependence of the summability properties of the datum f and of the initial datum $u_0$. The case of only summable data f and $u_0$ is allowed. We prove that these equations satisfy surprising regularization phenomena. Moreover we prove estimates (depending continuously from the data) that for zero datum f become well known decay (or ultracontractive) estimates.

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