Electron. J. Diff. Eqns., Vol. 1998(1998), No. 11, pp. 1-8.

Barriers on cones for degenerate quasilinear elliptic operators

Michail Borsuk & Dmitriy Portnyagin

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:
$$ {d\over dx_i}(|x|^\tau|u|^q|\nabla u|^{m-2}u_{x_i})= \mu |x|^\tau{|u|}^{q-1}\,{\rm sgn\,}u|\nabla u|^m\,,$$
$-1 less than \mu \leq 0\,,\quad q\geq 0\,,\quad m greater than 1 \,,\quad\tau greater than m-n$.

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.

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Note This article is related to another article published by the EJDE. Michail Borsuk & Dmitriy Portnyagin, On the Dirichlet problem for quasilinear elliptic second order equations with triple degeneracy and singularity in a domain with a boundary conical point , Vol. 1999(1999), No. 23, pp. 1-25.

photo Michail Borsuk
Department of Applied Mathematics
Olsztyn University of Agriculture and Technology
10-957 Olsztyn-Kortowo, Poland
e-mail: borsuk@art.olsztyn.pl
photo Dmitriy Portnyagin
Department of Physics, Lvov State University
290602 Lvov, Ukraine

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