报告时间：2025年9月10日（周三）下午17:00-18:00

报告地点：国交2号楼201会议室

报告人：Isabella Ianni 罗马大学（Sapienza University of Rome）

摘要：We present uniqueness and nondegeneracy results for non-negative solutions of semilinear equations with a power nonlinearity, set in bounded domains with Dirichlet boundary conditions.

We start discussing the local case where, for the planar Lane-Emden problem, we can give a positive answer to a longstanding uniqueness conjecture in convex domains. Furthermore, in planar non-convex domains we can show a local uniqueness result.

Then we also consider a nonlocal fractional version of the problem, where new difficulties arise, and we are able to show uniqueness for least energy solutions in balls or in more general symmetric domains.