In this paper, we discuss boundary value problems for a class of
nonlinear elliptic equations with data on a boundary surface. We
denote by y the unknown function which is supposed to take its values
in R^k. We assume that only some components of y are given on
the whole boundary surface implying the designation of nonregular
boundary value problems. To derive an interesting necessary condition
for the solvability of our original problem, we construct an appropriate
Cauchy problem for nonlinear elliptic equations which we solve by
making use of a parameter ε which is small enough.

nonlinear PDE, Cauchy problem, elliptic operators