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arXiv · 1906.10906

Improved H\"older regularity for strongly elliptic PDEs

Kari Astala·Albert Clop·Daniel Faraco·Jarmo Jääskeläinen·Aleksis Koski
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Abstract

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 H\"older regularity, higher than what is given by the classical exponent $1/K$.

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Kari Astala, Albert Clop, Daniel Faraco, Jarmo Jääskeläinen, Aleksis Koski. 2019-06-26. Improved H\"older regularity for strongly elliptic PDEs. https://doi.org/10.1016/j.matpur.2020.06.005

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