Global gradient estimates for general nonlinear elliptic measure data problems with Orlicz growth
Global gradient estimates for general nonlinear elliptic measure data problems with Orlicz growth
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DOI：
10.1016/j.jmaa.2023.127080
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发表时间：
2023-02
影响因子：
1.3
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
我们为 SOLA 的梯度提供了一个最优的全局 Calderón-Zygmund 理论到一般非线性椭圆方程 − div A (x, u, Du)= μ ，其主要部分取决于解本身，右侧数据 μ 是带符号的氡测量。假设相关的非线性 A 满足 x 中的 (δ, R 0)-BMO 条件、u 中的局部均匀连续性和 Du 中的 Orlicz 生长条件，同时假设底层域的边界为 Reifenberg 平坦。这是通过采用扰动方法并开发单参数技术以及应用最大函数自由技术来实现的。
We provide an optimal global Calderón-Zygmund theory for gradients of SOLAs to general nonlinear elliptic equations− div A (x, u, D u)= μ whose principle part depends on the solution itself and right-hand data μ is a signed Radon measure. The associated nonlinearity A is assumed to satisfy the (δ, R 0)-BMO condition in x, local uniform continuity in u, and Orlicz growth condition in Du, while the boundary of underlying domain is assumed to be Reifenberg flat. This is achieved by employing a perturbation method together with developing a one-parameter technique and by applying the maximal function free technique.