TANGENTIAL LIMITS OF MONOTONE SOBOLEV FUNCTIONS

Tangential limits have been discussed by several authors for harmonic functions with finite Dirichlet integral. This paper deals mostly with tangential limits for monotone functions in the half space of R(n), which are extensions of monotone functions on the one dimensional space R(1). Harmonic functions together with solutions in a wider class of nonlinear elliptic equations are monotone in our sense; of course, the coordinate functions of quasiregular mappings are monotone. We first give the fine limit result for Sobolev functions, and then apply the estimate of the oscillations over balls by the p-th means of partial derivatives over balls.