Singularities In L p-quasidisks

TL;DR

This paper investigates the boundary singularities of planar domains called cusps, and establishes a sharp integrability condition for the distortion function to determine the energy needed to smooth these singularities.

Contribution

It provides a precise criterion linking boundary cusp singularities and the integrability of the distortion function in quasidisks.

Findings

Established a sharp integrability condition for the distortion function.

Connected boundary cusp singularities with elastic energy required for smoothing.

Provided insights into the geometric and analytical properties of quasidisks.

Abstract

We study planar domains with exemplary boundary singularities of the form of cusps. A natural question is how much elastic energy is needed to flatten these cusps; that is, to remove singularities. We give, in a connection of quasidisks, a sharp integrability condition for the distortion function to answer this ques tion.