部分超定椭圆问题对称性的反例
Counterexamples to Symmetry for Partially Overdetermined Elliptic Problems
摘要：
我们展示了几个反例表明，著名的Serrin的对称性半线性椭圆超定问题的结果可能不成立的部分超定问题，也就是说，当Dirichlet和Neumann边界条件只规定的部分边界。我们的反例启发了前两位作者对这类部分超定组的正对称性结果，并证明了他们的假设。
英文摘要：
We exhibit several counterexamples showing that the famous Serrin's symmetry result for semilinear elliptic overdetermined problems may not hold for partially overdetermined problems, that is when both Dirichlet and Neumann boundary conditions are prescribed only on part of the boundary. Our counterexamples enlighten subsequent positive symmetry results obtained by the first two authors for such partially overdetermined systems and justify their assumptions as well.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
