Regularity of solutions of quasi-linear elliptic equations with [formula omitted] coefficients

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Let D be an bounded region in Rn. The regularity of solutions of a family of quasilinear elliptic partial differential equations is studied, one example being Δnu=Vun−1. The coefficients are assumed to be in the space Llogm⁡L(D) for m>n−1. Using a Moser iteration argument coupled with the Moser-Trudinger inequality, a local L∞ bound on the solution u is proven. A Harnack-type inequality is then proven. These results are shown to be sharp with respect to m. Then essential continuity of u is proven, and away from the boundary a bound on the modulus of continuity.