TY - JOUR
AU - V. M. Los’
PY - 2017/03/25
Y2 - 2023/12/08
TI - Systems parabolic in Petrovskii's sense in Hörmander spaces
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 69
IS - 3
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1702
AB - We study a general parabolic initial-boundary-value problem for systems parabolic in Petrovskii’s sense with zero initialCauchy data in some anisotropic H¨ormander inner-product spaces.We prove that the operators corresponding to this problemare isomorphisms between the appropriate H¨ormander spaces. As an application of this result, we establish a theorem onthe local increase in regularity of solutions of the problem. We also obtain new sufficient conditions of continuity for thegeneralized partial derivatives of a given order of a chosen component of the solution.
ER -