Multi-phase k-quadrature domains and applications to acoustic waves and magnetic fields

Pu-Zhao Kow () and Henrik Shahgholian ()
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Pu-Zhao Kow: National Chengchi University
Henrik Shahgholian: KTH Royal Institute of Technology

Partial Differential Equations and Applications, 2024, vol. 5, issue 3, 1-28

Abstract: Abstract The primary objective of this paper is to explore the multi-phase variant of quadrature domains associated with the Helmholtz equation, commonly referred to as k-quadrature domains. Our investigation employs both the minimization problem approach, which delves into the segregation ground state of an energy functional, and the partial balayage procedure, drawing inspiration from the recent work by Gardiner and Sjödin. Furthermore, we present practical applications of these concepts in the realms of acoustic waves and magnetic fields.

Keywords: Quadrature domain; Variational problem; Partial balayage; Non-scattering phenomena; Helmholtz equation; Acoustic waves; Magnetic fields; 35J05; 35J15; 35J20; 35R30; 35R35 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s42985-024-00283-1

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