Weighted Lorentz estimates for fully nonlinear elliptic equations with oblique boundary data
Weighted Lorentz estimates for fully nonlinear elliptic equations with oblique boundary data
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DOI：
10.1007/s41808-022-00151-2
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发表时间：
2022-02
影响因子：
0.8
通讯作者：
Junjie Zhang;Shenzhou Zheng
中科院分区：
文献类型：
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作者：
Junjie Zhang;Shenzhou Zheng
本文研究了具有斜边界条件的完全非线性椭圆型问题黏性解的加权Lorentz正则性，其条件是非线性f对x变量具有小的BMO半模，下域的边界属于某些。通过构造近似斜导数问题序列并在边界上平坦化覆盖参数，得到了加权洛伦兹空间中最优的全局Calderón-Zygmund型估计。作为主要定理的直接推论，我们还导出了变指数Morrey空间解的Hessian的整体正则性。
We devote this paper to the weighted Lorentz regularity of Hessian for viscosity solution of fully nonlinear elliptic problem with oblique boundary conditionunder the assumption that the nonlinearityFhas small BMO semi-norms with respect tox-variable and the boundary of underlying domain belongs tofor some. An optimal global Calderón–Zygmund type estimate in the weighted Lorentz spaces is obtained by constructing the sequence of approximating oblique derivative problems and flattening cover argument on the boundary. As a direct consequence of main theorem, we also derive global regularity in the variable exponent Morrey spaces to the Hessian of solution.