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Multiphase quadrature domains (existence and uniqueness)
Pu-Zhao Kow, Henrik Shahgholian, Tomas Sjödin
The primary goal of this paper is to give a precise definition and prove existence and uniqueness of multiphase quadrature domains for subharmonic functions, ensuring that the pres…
Inverse problems for the spectral fractional Laplacian with inhomogeneous Dirichlet boundary data
Ravi Shankar Jaiswal, Pu-Zhao Kow, Suman Kumar Sahoo
In this paper, we study the spectral fractional Laplacian with inhomogeneous Dirichlet boundary data. Our contributions are twofold: first we introduce a Dirichlet-to-Neumann map f…
Existence and regularity of minimizers for a variational problem of species population density
Pu-Zhao Kow, Masato Kimura, Hiroshi Ohtsuka
We study a variational problem motivated by models of species population density in a nonhomogeneous environment. We first analyze local minimizers and the structure of the saturat…
On scattering behavior of corner domains with anisotropic inhomogeneities: part II
Pu-Zhao Kow, Mikko Salo, Henrik Shahgholian
We study the scattering behavior of an anisotropic inhomogeneous Lipschitz medium at a fixed wave number, continuing our previous work [SIAM J. Math. Anal., 56(4):4834-4853, 2024]…
An inverse problem for semilinear elliptic equations with generalized Kerr-type nonlinearities
Pu-Zhao Kow, Rulin Kuan
We study the inverse problem of reconstructing the shape of unknown inclusions in semilinear elliptic equations with nonanalytic nonlinearities, by extending Ikehata's enclosure me…
Increasing resolution and instability for linear inverse scattering problems
Pu-Zhao Kow, Mikko Salo, Sen Zou
In this work we study the increasing resolution of linear inverse scattering problems at a large fixed frequency. We consider the problem of recovering the density of a Herglotz wa…