124 citations · 137 across the 10 of their papers we have counts for
4 papers · 1 filter
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…
A characterisation of harmonic functions by quadrature identities of annular domains and related results
Nikolay Kuznetsov
A new characterization of harmonic functions is obtained. It is based on quadrature identities involving mean values over annular domains and over concentric spheres lying within t…
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…