TY - JOUR
AU - V. M. Los’
PY - 2016/11/25
Y2 - 2024/04/15
TI - Sufficient conditions under which the solutions of general parabolic initial-boundaryvalue
problems are classical
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 68
IS - 11
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1938
AB - We establish new sufficient conditions under which the generalized solutions of initial-boundary-value problems for thelinear parabolic differential equations of any order with complex-valued coefficients are classical. These conditions areformulated in the terms of belonging of the right-hand sides of this problem to certain anisotropic H¨ormander spaces. Inthe definition of classical solution, its continuity on the line connecting the lateral surface with the base of the cylinder (inwhich the problem is considered) is not required.
ER -