Weak solutions of some quasilinear elliptic equations with data measures
Weak solutions of some quasilinear elliptic equations with data measures
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DOI：
10.1137/0524002
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发表时间：
1993
影响因子：
2
通讯作者：
N. Alaa;M. Pierre
中科院分区：
文献类型：
--
作者：
N. Alaa;M. Pierre
研究了一类具有数据测度和关于梯度的任意增长的拟线性椭圆方程弱解的存在唯一性。通常基于先验的$L_\infty $ -边界解及其梯度的技术不适用，因此需要一种新的方法。得到数据存在的各种必要或充分条件。考虑了超解与解的存在性之间的关系。最后给出了弱解的锐唯一性结果。
Existence and uniqueness of weak solutions for some quasilinear elliptic equations with data measures and arbitrary growth with respect to the gradient are studied. Usual techniques based on a priori $L_\infty $-bounds for the solutions and its gradient do not apply so that a new approach is needed. Various necessary or sufficient conditions are obtained on the data for existence. Relationship between existence of supersolutions and solutions is considered. Finally, sharp uniqueness results for weak solutions are given.