TY - JOUR
AU - T. M. Kasirenko
AU - A. A. Murach
PY - 2017/11/25
Y2 - 2022/10/05
TI - Elliptic problems with boundary conditions of higher orders in Hörmander spaces
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 69
IS - 11
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1797
AB - In a class of inner product H¨ormander spaces, we study a general elliptic problem for which the maximum order of theboundary conditions is not smaller than the order of the elliptic equation. The role of the order of regularity of these spacesis played by an arbitrary radial positive function $R_O$-varying at infinity in the sense of Avakumovi´c. We prove that theoperator of the problem under investigation is bounded and Fredholm on the appropriate pairs of the indicated H¨ormanderspaces. A theorem on isomorphism generated by this operator is proved. For the generalized solutions of this problem, weestablish a local a priori estimate and prove the theorem on the local regularity of these solutions in H¨ormander spaces. Asan application, we establish new sufficient conditions of continuity for the given generalized derivatives of the solutions.
ER -