Systems parabolic in Petrovskii's sense in Hörmander spaces

  • V. M. Los’

Abstract

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.
Published
25.03.2017
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, http://umj.imath.kiev.ua/index.php/umj/article/view/1702.
Section
Research articles