One-dimensionality of solutions of semilinear elliptic problems in cylindrical domains

Let omega be a bounded domain in Rn-1 with smooth boundary: a > 0, u+/- is an element of R; and let u is an element of C-1([-a, a] x <(omega)over bar> ) satisfy -del(g(\del u\) \del u\(-1) del u()) = f(x(1), u) and u(x1) great er than or equal to 0 in (-a, a) x omega, = u+/- on {+/-a} x omega and part ial derivative u/partial derivative v = 0 on (-a, a) x partial derivative o mega, where g is an element of C(R-0(+)) is nondecreasing, g(t) > 0 if t > 0 and f is continuous and nondecreasing an x(1). Using a rearrange ment ine quality we prove that u is a function of x(1) only. MSC (1991): 35B05, 35B5 0, 35B99, 35J25.