Failure of Fatou type theorems for solutions to PDE of p -Laplace type in domains with flat boundaries
Failure of Fatou type theorems for solutions to PDE of p -Laplace type in domains with flat boundaries
复制标题
平坦边界域中 p -拉普拉斯型偏微分方程解法图型定理的失败
DOI：
10.1080/03605302.2022.2056704
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发表时间：
2022
影响因子：
1.9
通讯作者：
Akman M
中科院分区：
文献类型：
--
作者：
Akman M
设为欧氏空间，给定正整数，设为k维平面，若我们首先研究p-Laplace方程解的Martin边值问题（称为p-调和函数），然后利用我们的研究结果，将Wolff关于p-调和函数的Fatou型定理的失败的工作推广到p-调和函数中，最后，我们讨论我们的工作的推广到p-Laplace型偏微分方程（所谓的调和函数）的解决方案。
Letdenote Euclideannspace and givenka positive integer letbe ak-dimensional plane withIfwe first study the Martin boundary problem for solutions to the p-Laplace equation (called p-harmonic functions) inrelative toWe then use the results from our study to extend the work of Wolff on the failure of Fatou type theorems for p-harmonic functions into p-harmonic functions inwhenFinally, we discuss generalizations of our work to solutions ofp-Laplace type PDE (called-harmonic functions).