For some anisotropic inner-product Hörmander spaces, we prove the theorems on well-posedness of initial-boundary-value problems for the two-dimensional heat-conduction equation with Dirichlet or Neumann boundary conditions. The regularity of the functions from these spaces is characterized by a couple of numerical parameters and a function parameter regularly varying at infinity in Karamata’s sense and characterizing the regularity of functions more precisely than in the Sobolev scale.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 5, pp. 645–656, May, 2015.
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Los’, V.M. Mixed Problems for the Two-Dimensional Heat-Conduction Equation in Anisotropic Hörmander Spaces. Ukr Math J 67, 735–747 (2015). https://doi.org/10.1007/s11253-015-1111-3
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DOI: https://doi.org/10.1007/s11253-015-1111-3