论文标题
具有规定的平均曲率的相变的各个方面
Variational aspects of phase transitions with prescribed mean curvature
论文作者
论文摘要
我们研究了利曼尼亚歧管中规定的平均曲率的相变的光谱。这些相变是对不均匀的半椭圆形PDE的解决方案，该椭圆形PDE产生了弥漫性对象（varifolds），该物体可能会限制为超出表面的奇异性，该物体的平均曲率由“规定的平均曲率曲率”功能确定，并确定其差异性。我们为扩散问题的特征值建立上限，以及当分散问题以多重性收敛时，更微妙的下限。对于后者，我们还建立了渐近的渐近级$ o（\ varepsilon^2）$和$ c^{2，α} $估计在多重性 - 一个相变层上的估计。
We study the spectrum of phase transitions with prescribed mean curvature in Riemannian manifolds. These phase transitions are solutions to an inhomogeneous semilinear elliptic PDE that give rise to diffuse objects (varifolds) that limit to hypersurfaces, possibly with singularities, whose mean curvature is determined by the "prescribed mean curvature" function and the limiting multiplicity. We establish upper bounds for the eigenvalues of the diffuse problem, as well as the more subtle lower bounds when the diffuse problem converges with multiplicity one. For the latter, we also establish asymptotics that are sharp to order $o(\varepsilon^2)$ and $C^{2,α}$ estimates on multiplicity-one phase transition layers.
