发表机构
School of Mathematics, Southeast University; Shing-Tung Yau Center of Southeast University; Southeast University; Shanghai Institute for Mathematics and Interdisciplinary Sciences（东南大学数学学院; 东南大学苏步青中心; 东南大学; 上海数学与交叉学科研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对带有退化权重等项的Hénon型无穷拉普拉斯方程，证明了退化集比较原理，建立了自由边界点的正则性与非退化估计，明确了解脱离零相位的速率。
AI 中文摘要
本工作研究带有退化权重、强吸收项和附加源项的无穷拉普拉斯驱动的Hénon型方程的非负粘性解。我们聚焦于位于权重退化集内的自由边界点，证明了退化集比较原理，该原理给出了由权重退化集上的值确定的每个切片内的唯一性，尽管一般情况下全局唯一性不成立。我们建立了自由边界点附近的精确改进正则性估计，其固有增长率为$r^{\frac{4+\alpha}{3-m}}$。最后，我们得到了自由边界点处匹配的非退化估计，该性质在非齐次情形下满足合适条件时成立，因此解以该速率脱离其零相位。
英文摘要
In this work, we study nonnegative viscosity solutions to Hénon-type equations driven by the infinity-Laplacian with a degenerate weight, strong absorption and an additional source term. We focus on free boundary points lying in the degeneracy set of the weight. We prove the degeneracy set comparison principle, which yields uniqueness within each slice determined by the value on the degeneracy set of the weight, although global uniqueness is not available in general. We establish sharp improved regularity estimates near free boundary points, with the intrinsic growth rate $r^{\frac{4+α}{3-m}}$. Finally, we obtain a matching non-degeneracy estimate at free boundary points; the property holds in the inhomogeneous case with suitable condition. Consequently, solutions detach from their zero phase at this rate.
Comments25 pages
