The Brezis–Nirenberg problem for systems involving divergence-form operators
The Brezis–Nirenberg problem for systems involving divergence-form operators
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DOI：
10.1007/s00030-023-00882-8
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发表时间：
2023-09
期刊：
影响因子：
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通讯作者：
Burton Brown;Mathew Gluck;Vince Guingona;Thomas Hammons;Miriam Parnes;Sean Pooley;Avery Schweitzer
中科院分区：
文献类型：
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作者：
Burton Brown;Mathew Gluck;Vince Guingona;Thomas Hammons;Miriam Parnes;Sean Pooley;Avery Schweitzer
我们研究涉及散度型算子的非线性椭圆偏微分方程组。所考虑的问题是经典 Brezis-Nirenberg 问题的自然推广。我们找到在域、耦合系数和微分算子系数上保证存在正解的条件以及在这些对象上不存在正解的条件。
We study a system of nonlinear elliptic partial differential equations involving divergence-form operators. The problem under consideration is a natural generalization of the classical Brezis–Nirenberg problem. We find conditions on the domain, the coupling coefficients and the coefficients of the differential operator under which positive solutions are guaranteed to exist and conditions on these objects under which no positive solution exists.