Vertical blow ups of capillary surfaces in . I: Convex corners.
Vertical blow ups of capillary surfaces in . II: Nonconvex corners.
Vortex rings for the Gross-Pitaevskii equation
We provide a mathematical proof of the existence of traveling vortex rings solutions to the Gross–Pitaevskii (GP) equation in dimension . We also extend the asymptotic analysis of the free field Ginzburg–Landau equation to a larger class of equations, including the Ginzburg–Landau equation for superconductivity as well as the traveling wave equation for GP. In particular we rigorously derive a curvature equation for the concentration set (i.e. line vortices if ).
Young measures as measurable functions and their applications to variational problems.
Zum Marx-Shiffmanschen Variationsproblem.
-convergence of discrete approximations to interfaces with prescribed mean curvature
The numerical approximation of the minimum problem: , is considered, where . The solution to this problem is a set with prescribed mean curvature and contact angle at the intersection of with . The functional is first relaxed with a sequence of nonconvex functionals defined in which, in turn, are discretized by finite elements. The -convergence of the discrete functionals to as well as the compactness of any sequence of discrete absolute minimizers are proven.
Γ-limits of convolution functionals
We compute the Γ-limit of a sequence of non-local integral functionals depending on a regularization of the gradient term by means of a convolution kernel. In particular, as Γ-limit, we obtain free discontinuity functionals with linear growth and with anisotropic surface energy density.
Исследование асимптотического поведения решения одной нестандартной вариационной задачи.
Минимизация функционалов, порождающих операторы кривизны
Многомерная задача Плато в римановых многообразиях
Решение одной изопериметрической задачи Полиа-Сеге
Три задачи о минимальных изотопиях и о приближении гомеоморфизмами кривых и поверхностей