Variational equations along integral curves of a projectable system of vector fields
Variational formulation for incompressible Euler flow/shape-morphing metric and geodesic
Variational problems and PDEs in affine differential geometry
This paper is part of the autumn school on "Variational problems and higher order PDEs for affine hypersurfaces". We discuss variational problems in equiaffine differential geometry, centroaffine differential geometry and relative differential geometry, which have been studied by Blaschke [Bla], Chern [Ch], C. P. Wang [W], Li-Li-Simon [LLS], and Calabi [Ca-II]. We first derive the Euler-Lagrange equations in these settings; these equations are complicated, strongly nonlinear fourth order PDEs. We...
Variational Problems with Non-Convex Obstacles an and Integral-Constraint for Vector-Valued Functions.
Variational Problems with Obstacles and a Volume Constraint.
Variations of additive functions
We study the relationship between derivates and variational measures of additive functions defined on families of figures or bounded sets of finite perimeter. Our results, valid in all dimensions, include a generalization of Ward’s theorem, a necessary and sufficient condition for derivability, and full descriptive definitions of certain conditionally convergent integrals.
Variationsprobleme vom Dirichlet-Typ mit einer Ungleichung als Nebenbedingung.
Vers un théorème de Skorohod simultané
Nous étudions un théorème de Skorohod pour des mesures vectorielles à valeurs . En notant la mesure image de par la variable aléatoire nous donnons des classes de mesures et éventuel-lement de variables telles que, si la suite converge étroitement, il existe une suite qui converge en mesure, éventuel-lement p.s.Le problème de Monge est abordé comme application. Soit la mesure variation de , pour un couple et une fonction coût le problème de Monge est l’existence d’une fonction...
Vertical blow ups of capillary surfaces in . I: Convex corners.
Vertical blow ups of capillary surfaces in . II: Nonconvex corners.
Verzweigungspunkte von H-Flächen. I.
Verzweigungspunkte von H-Flächen. II .
Volumes transverses aux feuilletages définissables dans des structures o-minimales.
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 ).
Weak and strong density results for the Dirichlet energy
Let be a smooth oriented Riemannian manifold which is compact, connected, without boundary and with second homology group without torsion. In this paper we characterize the sequential weak closure of smooth graphs in with equibounded Dirichlet energies, being the unit ball in . More precisely, weak limits of graphs of smooth maps with equibounded Dirichlet integral give rise to elements of the space (cf. [4], [5], [6]). In this paper we prove that every element in is the weak limit...
Weak shape formulation of free boundary problems
Weakly starlike logharmonic mappings.
Weierstrass-type representation of weakly regular pseudospherical surfaces in Euclidean space.
Weight minimization of elastic bodies weakly supporting tension. I. Domains with one curved side
Shape optimization of a two-dimensional elastic body is considered, provided the material is weakly supporting tension. The problem generalizes that of a masonry dam subjected to its own weight and to the hydrostatic presure. Existence of an optimal shape is proved. Using a penalty method and finite element technique, approximate solutions are proposed and their convergence is analyzed.
Whitney-type theorems on extension of functions on Carnot groups.