Electron. J. Diff. Eqns., Vol. 1999(1999), No. 23, pp. 1-25.

On the Dirichlet problem for quasilinear elliptic second order equations with triple degeneracy and singularity in a domain with a boundary conical point

Michail Borsuk & Dmitriy Portnyagin

In this article we prove boundedness and Holder continuity of weak solutions to the Dirichlet problem for a second order quasilinear elliptic equation with triple degeneracy and singularity. In particular, we study equations of the form
$-{d \over dx_i} (|x|^\tau |u|^q |\nabla u|^{m-2} u_{x_i})+
{a_0|x|^\tau  \over (x_{n-1}^2+x_n^2)^{m/2}} u|u|^{q+m-2} -\mu |x|^\tau u |u| ^{q-2} |\nabla u|^m 
 =f_0(x)-{\partial f_i \over \partial x_i}, $
with $a_0 \ge 0$, $q\ge 0$, $0\le \mu$ < 1, 1 < $m\le n$, and $\tau$ > m-n in a domain with a boundary conical point. We obtain the exact Holder exponent of the solution near the conical point.

Submitted April 23, 1999. Published June 24, 1999.
Math Subject Classification: 35B45, 35B65, 35D10, 35J25, 35J60, 35J65, 35J70.
Key Words: quasilinear elliptic degenerate equations, barrier functions, conical points.

Show me the PDF file (245K), TEX file, and other files for this article.

Note This article is related to another article published by EJDE. Michail Borsuk & Dmitriy Portnyagin, Barriers on cones for degenerate quasilinear elliptic operators, Vol. 1998(1998), No. 11, pp. 1-8.

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
e-mail: mitport@hotmail.com

Return to the EJDE web page