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Optimal regularity for $A$-harmonic type equations under the natural growth

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  • In this paper we are concerned with a class of nonlinear degenerate elliptic equations under the natural growth. We show that each bounded weak solution of $A$-harmonic type equations under the natural growth belongs to local Hölder continuity based on a density lemma and the Moser-Nash's argument. Then we show that its weak solution is of optimal regularity with the Hölder exponent for any $\gamma$: $0\le \gamma<\kappa$, where $\kappa$ is the same as the Hölder's index for homogeneous $A$-harmonic equations.
    Mathematics Subject Classification: Primary: 35J60; Secondary: 35B45, 35D30.

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