毛细泛函等容极值的存在性
Existence of isovolumetric extremals for capillarity functionals
摘要：
毛细泛函是定义在R3中的二维参数曲面类上的参数不变泛函，其形式为面积积分和适当形式的非齐次项之和。在这里，我们考虑的情况下，一类非齐次项消失在无穷远相应的毛细泛函没有体积约束的S2型极小曲面。利用变分技巧，我们证明了鞍型临界点极值的存在性。
英文摘要：
Capillarity functionals are parameter invariant functionals defined on classes of two-dimensional parametric surfaces in R3 as the sum of the area integral and a non homogeneous term of suitable form. Here we consider the case of a class of non homogenous terms vanishing at infinity for which the corresponding capillarity functional has no volume-constrained S2-type minimal surface. Using variational techniques, we prove existence of extremals characterized as saddle-type critical points.
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