GENERALIZED BOUNDARY VALUES OF THE SOLUTIONS OF SEMILINEARELLIPTIC EQUATIONS FROM WEIGHTED FUNCTIONAL SPACES

摘要

In weighted C-spaces, we establish the solvability of a boundary-value problem for a semilinear ellipticequation of order 2m in a bounded domain with generalized functions given on its boundary, strong powersingularities at some points of the boundary, and finite orders of singularities on the entire boundary. Thebehavior of the solution near the boundary of the domain is analyzed.