Electronic Journal of Differential Equations,
Vol. 1998(1998), No. 11, pp. 1-8.
Title: Barriers on cones for degenerate quasilinear elliptic operators
Authors: Michail Borsuk (Olsztyn Univ., Poland)
Dmitriy Portnyagin (Lvov State Univ., Ukraine)
Abstract:
Barrier functions $w=|x|^\lambda \Phi(\omega)$ 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:
$$ {d\over dx_i}(|x|^\tau|u|^q|\nabla u|^{m-2}u_{x_i})=
\mu |x|^\tau{|u|}^{q-1}\,{\rm sgn\,}u|\nabla u|^m\,,$$
$$-1<\mu \leq 0\,,\quad q\geq 0\,,\quad m>1\,,\quad\tau>m-n\,.$$
Submitted May 15, 1997. Published April 17, 1998.
Math Subject Classification: 35J65, 35J70, 35B05, 35B45, 35B65.
Key Words: quasilinear elliptic equations; barrier functions;
conical points.