Some questions about the regularity and the uniqueness of solutions of parabolic partial differential equations

Abstract

This work obtains a fixed-point equation for the solution of linear parabolic partial differential problems based on solutions to heat problems. This is a pointwise equality, so we have required non-standard techniques that involve the study of the sign of certain solutions to linear parabolic problems. This fixed-point equation implies regularity properties of solutions to parabolic problems, not necessarily linear, and this allows us to prove the uniqueness of the solution in three dimensions for the Navier-Stokes problem.