Singular quasilinear elliptic equations and Hölder regularity

We prove the Hölder regularity (Theorem 2.1) for weak solutions to singular quasilinear elliptic equations whose prototype is { − Δ p u = K ( x ) u δ + g ( x ) in Ω ; u | ∂ Ω = 0 , u > 0 in Ω , where Ω is an open bounded domain with smooth boundary, 1 p ∞ , δ > 0 , K ∈ L loc ∞ ( Ω ) satisfies 0 ⩽ K ( x ) ⩽ const ⋅ dist ( x , ∂ Ω ) − ω for a.e. x ∈ Ω , 0 ω 1 + ( 1 − δ ) ( 1 − 1 p ) , and 0 ⩽ g ∈ L ∞ ( Ω ) . Theorem 2.1 together with the Schauder fixed point theorem can be used to obtain the existence of weak solutions to the singular quasilinear elliptic system (PS) described in the Introduction.