blow-up phenomena 1conformal geometry 1ellipticity 1nonlinear pde 1sigma_2-yamabe equation 1sphere metrics 1
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math.AP2025
On the Schiffer and Berenstein conjectures with high-frequency for convex domains in the plane
Guowei Dai, Yingxin Sun, Juncheng Wei +1
In this paper, by introducing two-point stationary-phase amplitude defect, we provide a partial positive answer to the Schiffer and Berenstein conjectures in . More p…
math.AP2025
Total masses of solutions to general Toda systems with singular sources
Debabrata Karmakar, Chang-Shou Lin, Zhaohu Nie +1
In this article we obtain total masses of solutions to the Toda system associated to a general simple Lie algebra with singular sources at the origin. The determination of such tot…
math.AP2025
Finite-time singularity formations for the Landau-Lifshitz-Gilbert equation in dimension two
Juncheng Wei, Qidi Zhang, Yifu Zhou
We construct finite time blow-up solutions to the Landau-Lifshitz-Gilbert equation (LLG) from into \begin{equation*} \begin{cases} u_t= a(Îu+|\nabla u|^2u) -…