3 papers
math.PR2026
Sobolev multipliers and fractional Gaussian fields on Lipschitz boundaries with applications to deterministic and random acoustic systems
Illya M. Karabash
Motivated by Applied Physics and Photonics studies of random resonators, we study in the stochastic part of this paper random acoustic operators in non-smooth bounded domains $G \s…
math.AP2025
M-dissipative generalized impedance boundary conditions, discrete spectra, and pointwise multipliers between fractional Sobolev spaces
Illya M. Karabash
The paper studies properties of acoustic operators in bounded Lipschitz domains with m-dissipative generalized impedance boundary conditions. We prove that such acoustic opera…
math.AP2024
Random acoustic boundary conditions and Weyl's law for Laplace-Beltrami operators on non-smooth boundaries
Illya M. Karabash
Motivated by engineering and photonics research on resonators in random or uncertain environments, we study rigorous randomizations of boundary conditions for wave equations of the…