We establish surprising improved Schauder regularity properties for solutions to the Leray-Lions divergence type equation in the plane. The results are achieved by studying the nonlinear Beltrami equation and making use of special new relations between these two equations. In particular, we show that solutions to an autonomous Beltrami equation enjoy a quantitative improved degree of Hölder regularity, higher than what is given by the classical exponent $1/K$.

中文翻译：

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改善强椭圆PDE的Hölder规律性

我们建立了令人惊讶的改进的Schauder正则性质，以解决平面中Leray-Lions发散型方程。通过研究非线性Beltrami方程并利用这两个方程之间的特殊新关系来获得结果。特别地，我们表明，自治的Beltrami方程的​​解在数量上改善了Hölder正则性程度，高于经典指数给出的程度。$\mathrm{1个}/ķ$。