On spatial energy decay for quasilinear boundary value problems in cone-like and exterior domains

A number of boundary value problems for second order quasilinear partial differential equations in divergence form, in cone-like domains and exterior domains, in two and three dimensions, are considered. For the cone-like domains, homogeneous data of either the Dirichlet, Neumann, or mixed type are prescribed on the lateral sides. New results are obtained concerning the spatial decay of the energy (Dirichlet norm of the solution) at infinity and its maximum rate of growth near the finite end of the domain.