Coarse Regularity of Solutions to a Nonlinear Sigma-model with~$L^p$~gravitino

TL;DR

This paper investigates the regularity of weak solutions to a 2D nonlinear sigma model with an $L^p$ gravitino, demonstrating how solution regularity varies with the integrability parameter $p$.

Contribution

It establishes new regularity results for solutions when the gravitino is only in $L^p$, extending previous understanding to lower regularity assumptions.

Findings

Regularity depends on the value of p

Solutions are more regular for higher p

New techniques handle low-regularity gravitino

Abstract

The regularity of weak solutions of a two-dimensional nonlinear sigma model with coarse gravitino is shown. Here the gravitino is only assumed to be in $L^p$ for some $p>4$. The precise regularity results depend on the value of $p$.