Optimal time and space regularity for solutions of degenerate differential equations

TL;DR

This paper establishes the best possible regularity results in time and space for solutions to a class of degenerate differential equations in Banach spaces, revealing a trade-off between spatial and temporal regularity.

Contribution

It provides the first optimal regularity estimates in both time and space for degenerate differential equations in Banach spaces, highlighting a prevalence of space regularity.

Findings

Optimal regularity in space and time derived

Higher space regularity corresponds to lower time regularity

Results demonstrate a prevalence of space regularity in solutions

Abstract

We derive optimal regularity, in both time and space, for solutions of the Cauchy problem related to a degenerate differential equation in a Banach space X. Our results exhibit a sort of prevalence for space regularity, in the sense that the higher is the order of regularity with respect to space, the lower is the corresponding order of regularity with respect to time.