Geodesic
On the Dirichlet problem for quasilinear elliptic second order equations with triple degeneracy and singularity in a domain with a boundary conical point
Electronic Journal of Differential Equations, Tome 1999 (1999).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 35B45, 35B65, 35D10, 35J25, 35J60, 35J65, 35J70
Keywords: quasilinear elliptic degenerate equations, barrier functions, conical points 
@article{EJDE_1999__1999__a37,
     author = {Borsuk, Michail and Portnyagin, Dmitriy},
     title = {On the {Dirichlet} problem for quasilinear elliptic second order equations with triple degeneracy and singularity in a domain with a boundary conical point},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {1999},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a37/}
}
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%J Electronic Journal of Differential Equations
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Borsuk, Michail; Portnyagin, Dmitriy. On the Dirichlet problem for quasilinear elliptic second order equations with triple degeneracy and singularity in a domain with a boundary conical point. Electronic Journal of Differential Equations, Tome 1999 (1999). http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a37/