Partial balayage for the Helmholtz equation

Kow, Larson, Salo and Shahgholian recently initiated the study of quadrature domains for the Helmholtz equation and developed an associated theory of partial balayage of measures. The present paper offers an alternative approach to partial balayage in this context that yields stronger results. Applications are given to quadrature domains and to a domain evolution question that is analogous to Hele-Shaw flow.