5 papers
On approximation theorems for solutions to strongly parabolic systems in anisotropic Sobolev spaces
Alexander Shlapunov, Pavel Vilkov
We investigate the problem on Runge pairs for Sobolev solutions of strongly uniformly parabolic systems in non-cylindrical domains of a special kind. We prove that if the coefficie…
The Grothendieck duality and sparse minimizing in spaces of Sobolev solutions to elliptic systems
Alexander Shlapunov, Alexander Polkovnikov, Kseniya Gagelgans
We present an instructive example of using Banach spaces of solutions to (linear, generally, non-scalar) elliptic operator to investigate variational inverse problems related t…
On the Grothendieck duality for the space of holomorphic Sobolev functions
Arkadii Levskii, Alexander Shlapunov
We describe the strong dual space for the space of holomorphic functions from the Sobolev space $H^s(D…
Maxwell's and Stokes' operators associated with elliptic differential complexes
Alexander Shlapunov, Alexander Polkovnikov, Victor Mironov
We propose a new technique to generate reasonable systems of partial differential equations (PDE) that could be potential candidates for depicting models in natural sciences relate…
On the Cauchy Problem for Elliptic Complexes in Spaces of Distributions
Alexander Shlapunov, Dmitrii Fedchenko
Let D be a bounded domain in n-dimensional Eucledian space with a smooth boundary. We indicate appropriate Sobolev spaces of negative smoothness to study the non-homogeneous Cauchy…