On the transmission problem for second-order quasilinear elliptic equations in divergence form

A statement of the transmission problem for quasilinear elliptic equations in divergence form in bounded composed domains in terms of the strengthened Sobolev spaces is proposed. Some generalized sufficient solvability conditions for the Dirichlet boundary value problem are obtained. A condition for which the “flow” is uniquely determined by the solution of the problem is derived. It is noted that the results of this study can be applied for investigations of nonlinear seepage theory problems in composed domains.