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math.AP2025
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…
math.AP2025
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…