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arXiv · 2011.10969

Up-to-boundary pointwise gradient estimates for very singular quasilinear elliptic equations with mixed data

Tan Duc Do·Le Xuan Truong·Nguyen Ngoc Trong
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Abstract

This paper establishes pointwise estimates up to boundary for the gradient of weak solutions to a class of very singular quasilinear elliptic equations with mixed data: \begin{cases} -\operatorname{div}(A(x,D u))=g-\operatorname{div} f \quad & \mathrm{in} \quad \Omega \\ u= 0 \quad & \text{on} \ \partial \Omega, \end{cases} where $\Omega \subset \mathbb{R}^n$ is sufficiently flat in the sense of Reifenberg.

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Tan Duc Do, Le Xuan Truong, Nguyen Ngoc Trong. 2020-11-22. Up-to-boundary pointwise gradient estimates for very singular quasilinear elliptic equations with mixed data. https://arxiv.org/abs/2011.10969

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