14 citations · 25 across the 27 of their papers we have counts for
31 papers
The fundamental eigenfrequency is simple in the two-dimensional sloshing problem
Nikolay Kuznetsov
The two-dimensional sloshing problem is considered; it describes the transversal free oscillations of water in an open, infinitely long canal of uniform cross-section. It is proved…
Two-dimensional sloshing: domains with interior `high spots'
Nikolay Kuznetsov, Oleg Motygin
Considering the two-dimensional sloshing problem, our main focus is to construct domains with interior high spots; that is, points, where the free surface elevation for the fundame…
Characterizations of discs via weighted means
Nikolay Kuznetsov
New theorems characterizing analytically discs in the Euclidean plane $\RR^2$ are proved. Weighted mean value properties of solutions to the modified Helmholtz equation and harmoni…
Mean value properties of solutions to the modified Helmholtz equation and related topics (a survey)
Nikolay Kuznetsov
Recent results concerning solutions of the modified Helmholtz equation are reviewed; namely, various mean value properties and their corollaries, converse and inverse of these prop…
On relations between harmonic functions and solutions of the modified Helmholtz equation
Nikolay Kuznetsov
We consider the -dimensional modified Helmholtz equation and establish two relations between its solutions in a bounded domain and harmonic functions. Both relations essentially…
"Potato kugel" for nuclear forces and a small one for acoustic waves
Nikolay Kuznetsov
The "potato kugel" theorem of Aharonov, Schiffer and Zalcman, which concerns an inverse property of harmonic functions, is extended to the settings of the modified Helmholtz and He…