Borsuk, MichailPortnyagin, Dmitriy2019-09-242019-09-241999-06-24Borsuk, 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. 1-25.1072-6691https://hdl.handle.net/10877/8647In 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.Text25 pages1 file (.pdf)enAttribution 4.0 InternationalQuasilinear elliptic degenerate equationsBarrier functionsConical pointsArticle