BEHAVIOR IN THE LIMIT, AS P-]INFINITY, OF MINIMIZERS OF FUNCTIONALS INVOLVING P-DIRICHLET INTEGRALS

The purpose of this paper is to study the behaviour, as p --> infinity , of minimizers of functionals involving p-Dirichlet integrals in a bo unded Lipschitz domain, Omega subset of R(n). In the case where R is a convex ring it is proved that the minimizers converge monotonically a nd uniformly. In the paper by T. Bhattacharya, E. DiBenedetto, and J. Manfredi [Limits as p --> infinity of Delta(p)u(p) = f and related ext remal problems, Rand. Sem. Mat. Univ. Politec. Torino, (1989), pp. 15- 68], the problem of torsional creep is studied. Here the situation is generalized by introducing a more general functional and relaxing the boundary conditions. Various aspects of the Green function of the p la placian are considered and it is proved that the Green function is not symmetric if p is sufficiently large. Finally, it is proved that the extremals to the dual problem tend to zero in the mean as p --> infini ty, outside a well-specified subset of R.