On the Dirichlet Problem for Quasilinear Elliptic Second Order Equations with Triple Degeneracy and Singularity in a Domain with a Boundary Conical Point
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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−2uxt) + α0|x|τ/(x2 n-1 + x2n)m/2 u|u|q+m-2 - µ|x|τ u|u|q-2|∇u|m = = fo(x) - ∂fi / ∂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.