Barriers on Cones for Degenerate Quasilinear Elliptic Operators

Abstract

Barrier functions w = |x|λΦ(ω) are constructed for the first boundary value problem as well as for the mixed boundary value problem for quasilinear elliptic second order equation of divergent form with triple degeneracy on the n-dimensional convex circular cone:

d/dxi (|x|τ |u|q |∇u|m-2uxi) = µ|x|τ|u|q-1sgn u|∇u|m,

where -1 < µ ≤ 0, q ≥ 0, m > 1, τ > m - n.