Systems parabolic in Petrovskii's sense in Hörmander spaces

  • V. M. Los’


We study a general parabolic initial-boundary-value problem for systems parabolic in Petrovskii’s sense with zero initial Cauchy data in some anisotropic H¨ormander inner-product spaces.We prove that the operators corresponding to this problem are isomorphisms between the appropriate H¨ormander spaces. As an application of this result, we establish a theorem on the local increase in regularity of solutions of the problem. We also obtain new sufficient conditions of continuity for the generalized partial derivatives of a given order of a chosen component of the solution.
How to Cite
Los’, V. M. “Systems Parabolic in Petrovskii’s Sense in Hörmander Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, no. 3, Mar. 2017, pp. 365-80,
Research articles