3 papers
math.AP2026
Matrix parabolic problems in Sobolev spaces of generalized smoothness
Valerii Los, Vladimir Mikhailets, Aleksandr Murach
We study a general linear parabolic problem for Petrovskii parabolic differential system in Sobolev anisotropic distribution spaces of generalized smoothness. Slowly varying functi…
math.AP2025
Elliptic boundary-value problems in some distribution spaces of generalized smoothness
Anna Anop, Aleksandr Murach
We build a solvability theory of elliptic boundary-value problems in normed Sobolev spaces of generalized smoothness for any integrability exponent . The smoothness is given b…
math.AP2025
Extended Sobolev scale for vector bundles, and its applications
Aleksandr Murach, Tetiana Zinchenko
We study an extended Sobolev scale for smooth vector bundles over a smooth closed manifold. This scale is built on the base of inner product distribution spaces of generalized smoo…