This open access book provides an extensive treatment of Hardy inequalities and closely
related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The …

We propose the analogues of boundary layer potentials for the sub-Laplacian on
homogeneous Carnot groups/stratified Lie groups and prove continuity results for them. In …

The inverse problem of reconstructing a source term from boundary measurements, for the
wave equation, is revisited. We propose a novel approach to recover the unknown source …

In this note we construct an integral boundary condition for the Kohn Laplacian in a given
domain on the Heisenberg group extending to the setting of the Heisenberg group M. Kac's …

This paper aims at understanding the nature of the subwavelength resonant frequencies of
dielectric particles with high refractive indices. It is proved that for an arbitrary shaped …

ON A NONLOCAL BOUNDARY VALUE PROBLEM FOR THE MULTIDIMENSIONAL HEAT
EQUATION IN A NONCYLINDRICAL DOMAIN Page 1 Siberian Mathematical Journal, Vol …

We deal with the photoacoustic imaging modality using dielectric nano-particles as contrast
agents. Exciting the heterogeneous tissue, localized in a bounded domain Ω, with an …

In this paper we develop an artificial initial boundary value problem for the high-order heat
equation in a bounded domain $\Omega $. It is found an unique classical solution of this …

Integral operators of the form L_K^-1 f (x)= ∫\limits_ Ω K (x, t) f (t) dt for the case of a finite
domain Ω⊂ R n with smooth boundary∂ Ω are considered. Conditions on the real kernel K …

We deal with the time-harmonic acoustic waves scattered by a large number of small holes,
with radius a, a≪ 1, arbitrarily distributed in a bounded part of the homogeneous …