Smoothing effect and regularity for linear parabolic equations

A Strong Regularity Result for Parabolic Equations

We consider a parabolic equation with a drift term u+b∇u−ut = 0. Under the condition divb = 0, we prove that solutions possess dramatically better regularity than those provided by standard theory. For example, we prove continuity of solutions when not even boundedness is expected.

Local Regularity Results for Some Parabolic Equations

In this paper we prove the local L s regularity (where s depends on the summability of the data) for local " unbounded " weak solutions of a class of nonlinear parabolic equations including the p-Laplacian equation.

Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations

A smoothing property in multistep backward difference method for a linear parabolic problem in Hilbert space has been proved, where the operator is selfadjoint, positive definite with compact inverse. By using the solutions computed by a multistep backward difference method for the parabolic problem, we introduce an approximation scheme for time derivative. The nonsmooth data error estimate for...

Higher regularity for parabolic equations and maximum principles

Regularity estimates for parabolic integro- differential equations and applications

We review some regularity results for integro-differential equations, focusing on Hölder estimates for equations with rough kernels and their applications. We show that if we take advantage of the integral form of the equation, we can obtain simpler proofs than for second order equations. For the equations considered here, the Harnack inequality may not hold. Mathematics Subject Classification ...