On approximation theorems for solutions to strongly parabolic systems in anisotropic Sobolev spaces

Alexander Shlapunov; Pavel Vilkov

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arXiv · 2511.15216

On approximation theorems for solutions to strongly parabolic systems in anisotropic Sobolev spaces

Alexander Shlapunov·Pavel Vilkov

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Abstract

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 coefficients of a parabolic operator are constant, then two domains with sufficiently smooth boundaries, no parts of which are parallel to the plane $t=0$, form a Runge pair if and only if the complements of any section of the larger domain to the section of the smaller domain by planes $t = const$, have no compact components in the larger section.

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Alexander Shlapunov, Pavel Vilkov. 2025-11-19. On approximation theorems for solutions to strongly parabolic systems in anisotropic Sobolev spaces. https://arxiv.org/abs/2511.15216

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