TY - JOUR
AU - K. O. Buryachenko
PY - 2011/08/25
Y2 - 2024/04/23
TI - Solvability of inhomogeneous boundary-value problems for fourth-order differential equations
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 63
IS - 8
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2781
AB - We consider a Cauchy-type boundary-value problem of, a problem with three boundary conditions, and the Dirichlet problem for a general fourth-order differential equation with constant complex coefficients and nonzero right-hand side in a bounded domain $\Omega \subset R^2$ with smooth boundary. Using the method of the Green formula, the theory of expansion of differential operators, and the theory of $L$-traces (i.e., traces associated with a differential operation $L$), we obtain necessary and sufficient (for elliptic operators) conditions for the solvability of each of the problems under consideration in the space $H^m(\Omega),\;\; m \geq 4$.
ER -