Variational aspects of phase transitions with prescribed mean curvature
Variational aspects of phase transitions with prescribed mean curvature
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DOI：
10.1007/s00526-021-02150-y
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发表时间：
2020-10
影响因子：
2.1
通讯作者：
Christos Mantoulidis
中科院分区：
文献类型：
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作者：
Christos Mantoulidis
我们研究黎曼流形中具有规定平均曲率的相变谱。这些相变是非齐次半线性椭圆偏微分方程的解，产生限制于超曲面的漫射物体（杂折），可能具有奇点，其平均曲率由“规定平均曲率”函数和极限重数确定。我们建立了扩散问题特征值的上限，以及当扩散问题收敛到重数一时的更微妙的下界。对于后者，我们还建立了在多重一相变层上易于有序和估计的渐近函数。
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 orderandestimates on multiplicity-one phase transition layers.