AI 中文总结
研究一类含垂直边界条件且强迫梯度爆破的Serrin型超定问题，确定其在球上有解的范围，证明在此范围内解域为球且解由明确径向分布唯一确定。
AI 中文摘要
我们研究了一类可能退化的椭圆算子在垂直边界条件下强迫梯度爆破的Serrin型超定问题。我们确定了问题在球上有解的精确范围。在此范围内，我们证明了刚性：每个解域都是一个球，并且解由一个明确的径向分布唯一确定。
英文摘要
We study Serrin-type overdetermined problems for a class of possibly degenerate elliptic operators under a vertical boundary condition forcing gradient blow-up. We identify the precise regime in which the problem admits a solution on a ball. In this regime, we prove rigidity: every solution domain is a ball, and the solution is uniquely determined by an explicit radial profile.
