Loss of derivatives in the infinite type

TL;DR

This paper investigates the phenomenon of loss of derivatives in the context of degenerate vector fields arising from infinite type exponentially non-degenerate hypersurfaces in complex two-dimensional space.

Contribution

It provides a detailed analysis of derivative loss phenomena specific to a class of hypersurfaces of infinite type, expanding understanding in complex analysis and PDEs.

Findings

Identifies conditions leading to loss of derivatives in these vector fields

Characterizes the nature of degeneracy in infinite type hypersurfaces

Provides theoretical insights into regularity issues in complex analysis

Abstract

We discuss loss of derivatives for degenerate vector fields obtained from infinite type exponentially non-degenerate hypersurfaces of $\C^2$.