Mixed Problems for the Two-Dimensional Heat-Conduction Equation in Anisotropic Hörmander Spaces
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.
English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 5, pp 735-747.
Citation Example: Los’ V. M. Mixed Problems for the Two-Dimensional Heat-Conduction Equation in Anisotropic Hörmander Spaces // Ukr. Mat. Zh. - 2015. - 67, № 5. - pp. 645-656.