On the Dirichlet Problem for Quasilinear Elliptic Second Order Equations with Triple Degeneracy and Singularity in a Domain with a Boundary Conical Point
Date
1999-06-24
Authors
Borsuk, Michail
Portnyagin, Dmitriy
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
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/dxi (|x|τ|u|q|∇u|m−2uxi) + α0|x|τ/(x2n-1 + x2n)m/2 u|u|q+m-2 - µ|x|τ u|u|q-2|∇u|m =
= ƒ0(x) - ∂ƒi / ∂xi,
with α0 ≥ 0, q ≥ 0, 0 ≤ µ < 1, 1 < m ≤ n, and τ > m − n in a domain with a boundary conical point. We obtain the exact Hölder exponent of the solution near the conical point.
Description
Keywords
Quasilinear elliptic degenerate equations, Barrier functions, Conical points
Citation
Borsuk, M., & Portnyagin, D. (1999). On the Dirichlet problem for quasilinear elliptic second order equations with triple degeneracy and singularity in a domain with a boundary conical point. <i>Electronic Journal of Differential Equations, 1999</i>(23), pp. 1-25.
Rights
Attribution 4.0 International