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Nonlinear boundary value problems relative to harmonic functions
Nonlinear Analysis ( IF 1.4 ) Pub Date : 2020-08-28 , DOI: 10.1016/j.na.2020.112090 Y. Oussama Boukarabila , Laurent Véron
中文翻译:
与谐波函数有关的非线性边值问题
更新日期:2020-08-28
Nonlinear Analysis ( IF 1.4 ) Pub Date : 2020-08-28 , DOI: 10.1016/j.na.2020.112090 Y. Oussama Boukarabila , Laurent Véron
We study the problem of finding a function verifying in under the boundary condition on where is a smooth domain, is the normal unit outward vector to , is a measure on and a continuous nondecreasing function. We give sufficient condition on for this problem to be solvable for any measure. When , , we give conditions in order an isolated singularity on to be removable. We also give capacitary conditions on a measure in order the problem with to be solvable for some . We also study the isolated singularities of functions satisfying and on .
中文翻译:
与谐波函数有关的非线性边值问题
我们研究寻找功能的问题 验证中 在 在边界条件下 上 哪里 是一个平滑的领域, 是法向单位向量 , 是对 和 连续的非递减函数。我们给充分条件该问题可以通过任何措施解决。什么时候, ,我们给出条件以使上的孤立奇点 可移动。我们还给出了一定的容量条件 为了解决问题 可以解决一些 。我们还研究了满足以下条件的函数的孤立奇异性 和 上 。