Conservation laws for even order systems of polyharmonic map type

TL;DR

This paper extends conservation law results to higher-order polyharmonic map systems, establishing continuity of weak solutions in critical dimensions, generalizing prior work on second and fourth order systems.

Contribution

It introduces conservation laws for even order systems of polyharmonic maps, broadening the understanding of weak solution regularity in higher dimensions.

Findings

Established conservation laws for order 2m systems.

Proved continuity of weak solutions under natural conditions.

Generalized previous results from second and fourth order cases.

Abstract

Following Rivi\`ere's study of conservation laws for second order quasilinear systems with critical nonlinearty and Lamm/Rivi\`ere's generalization to fourth order, we consider similar systems of order $2m$. Typical examples are $m$-polyharmonic maps. Under natural conditions, we find a conservation law for weak solutions on $2m$-dimensional domains. This implies continuity of weak solutions.