Related papers: Coisotropic Variational Problems
This survey on stationary and evolutionary problems with gradient constraints is based on developments of monotonicity and compactness methods applied to large classes of scalar and vectorial solutions to variational and quasi-variational…
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…
The Lagrange problem is established in the discrete field theory subject to constraints with values in a Lie group. For the admissible sections that satisfy a certain regularity condition, we prove that the critical sections of such…
This work explores the tensor and combinatorial constructs underlying the linearised higher-order variational equations of a generic autonomous system along a particular solution. The main result of this paper is a compact yet explicit and…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
We present a general method for the analysis of the stability of static, spherically symmetric solutions to spherically symmetric perturbations in an arbitrary diffeomorphism covariant Lagrangian field theory. Our method involves fixing the…
Automatically determining the number of intrinsic mode functions (IMFs) and their center frequencies in Variational Mode Decomposition (VMD) remains an open mathematical challenge. Existing methods rely on heuristic settings,…
We interpret all Maurer-Cartan elements in the formal Hochschild complex of a small dg category which is cohomologically bounded above in terms of torsion Morita deformations. This solves the "curvature problem", i.e. the phenomenon that…
For a hypersurface V of a conformal space, we introduce a conformal differential invariant I = h^2/g, where g and h are the first and the second fundamental forms of V connected by the apolarity condition. This invariant is called the…
We show that for n>2 the following equivalence problems are essentially the same: the equivalence problem for Lagrangians of order n with one dependent and one independent variable considered up to a contact transformation, a multiplication…
The objective of this work is to establish a systematic study of boundary value problems within the framework of differential forms and variable exponent spaces. Specifically, we investigate the Hodge Laplacian and related first order…
We consider an optimal control problem governed by an elliptic variational inequality of the second kind. The problem is discretized by linear finite elements for the state and a variational discrete approach for the control. Based on a…
We investigate symmetry reduction of optimal control problems for left-invariant control systems on Lie groups, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles and considers a…
In this paper, we solve some constrained variational problems on perturbed lattice graphs $G$. The first problem addresses the existence of ground state normalized solutions to Schr\"odinger equations \begin{equation*} \left\{…
We study some approximation problems on a strict subset of the circle by analytic functions of the Hardy space H2 of the unit disk (in C), whose modulus satisfy a pointwise constraint on the complentary part of the circle. Existence and…
For an embedded conformal hypersurface with boundary, we construct critical order local invariants and their canonically associated differential operators. These are obtained holographically in a construction that uses a singular Yamabe…
We consider natural conformal invariants arising from the Gauss-Bonnet formulas on manifolds with boundary, and study conformal deformation problems associated to them. The key technique we used is to derive boundary C^2 estimates directly…
This paper provides necessary and sufficient conditions of optimality for variational problems that deal with a fractional derivative with respect to another function. Fractional Euler--Lagrange equations are established for the fundamental…
In this paper, we study the symmetry properties of nondegenerate critical points of shape functionals using the implicit function theorem. We show that, if a shape functional is invariant with respect to some continuous group of rotations,…
In the theory of submanifolds, the following problem is fundamental: to establish simple relationships between the main intrinsic invariants and the main extrinsic invariants of the submanifolds.The basic relationships discovered until now…