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Higher Regularity of Homogeneous Gradient Compositions for $p$-Laplace-Type Equations
In this paper, we study higher regularity of homogeneous functions of the gradient of solutions to the inhomogeneous $p$-Laplace equation $\operatorname{div}(|Du|^{p-2}Du)=f$. Although a solution need not be of class $C^2$ across its critical set, its gradient is locally H\"older continuous. Suppose that $Du\in C^{0,\a...