ﻻ يوجد ملخص باللغة العربية
We review classical results where the method of the moving planes has been used to prove symmetry properties for overdetermined PDEs boundary value problems (such as Serrins overdetermined problem) and for rigidity problems in geometric analysis (like Alexandrov soap bubble Theorem), and we give an overview of some recent results related to quantitative studies of the method of moving planes, where quantitative approximate symmetry results are obtained.
The system leading to phase segregation in two-component Bose-Einstein condensates can be generalized to hyperfine spin states with a Rabi term coupling. This leads to domain wall solutions having a monotone structure for a non-cooperative system. We
Suppose $uin dot{H}^1(mathbb{R}^n)$. In a seminal work, Struwe proved that if $ugeq 0$ and $|Delta u+u^{frac{n+2}{n-2}}|_{H^{-1}}:=Gamma(u)to 0$ then $dist(u,mathcal{T})to 0$, where $dist(u,mathcal{T})$ denotes the $dot{H}^1(mathbb{R}^n)$-distance of
Alexandrovs soap bubble theorem asserts that spheres are the only connected closed embedded hypersurfaces in the Euclidean space with constant mean curvature. The theorem can be extended to space forms and it holds for more general functions of the p
We propose a unified method for the large space-time scaling limit of emph{linear} collisional kinetic equations in the whole space. The limit is of emph{fractional} diffusion type for heavy tail equilibria with slow enough decay, and of diffusive ty
Let $(mathcal{M},g_0)$ be a compact Riemannian manifold-with-boundary. We present a new proof of the classical Gaffneys inequality for differential forms in boundary value spaces over $mathcal{M}$, via the variational approach `{a} la Kozono--Yanagis