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

2025/05/28 by Delgado, Inmaculada Gayte, Gayte, Irene Marín
#35Q30 #49K20 #76D05 #93C95 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.22110

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.

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