AI 中文总结
该研究针对柱体上加权退化/奇异问题，用Almgren型方法推导Robin方程边缘渐近性，将其应用于谱分数阶拉普拉斯算子，得到局部渐近性、唯一延拓及统一的局部衰减率量化结果。
AI 中文摘要
针对柱体上的一类加权退化或奇异问题，采用Almgren型单调性方法推导了基底面与侧面交界面边缘附近解的渐近估计，该交界面施加Robin边界条件。作为相关应用，得到了Robin和Neumann谱分数阶拉普拉斯算子的局部渐近性及从边界的唯一延拓。Neumann与Robin问题解的局部衰减率相同，且由具有某种对称性的加权球面谱问题明确量化。
英文摘要
For a class of weighted degenerate or singular problems on a cylinder, Almgren-type monotonicity methods are employed to derive asymptotic estimates of solutions near the edge between the base and the lateral surface, where a Robin boundary condition is imposed. As a relevant application, local asymptotics and unique continuation from the boundary are obtained for the Robin and Neumann spectral fractional Laplacians. The local decay rates of the solutions are the same for both the Neumann and the Robin problems and are explicitly quantized by a weighted spherical spectral problem with some symmetry.
Comments41 pages, 1 figure
