A general approach for multiconfiguration method sin quantum molecular chemistry
A general class of phase transition models with weighted interface energy
A generalization of the saddle point method with applications
We show that one can drop an important hypothesis of the saddle point theorem without affecting the result. We then show how this leads to stronger results in applications.
A Note on the Problem -...u = ...u + u| u|2*-2.
A numerical minimization scheme for the complex Helmholtz equation
We use the work of Milton, Seppecher, and Bouchitté on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In particular, this method results in a finite element matrix that is symmetric positive-definite and therefore simple iterative descent methods and preconditioning can be used to solve the resulting system of equations. We also derive an error bound for the method and illustrate...
A numerical minimization scheme for the complex Helmholtz equation
We use the work of Milton, Seppecher, and Bouchitté on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In particular, this method results in a finite element matrix that is symmetric positive-definite and therefore simple iterative descent methods and preconditioning can be used to solve the resulting system of equations. We also derive an error bound for the method and illustrate...
A posteriori estimations of approximate solutions for some types of boundary value problems
A rigorous derivation of free-boundary problem arising in superconductivity
A Variational Approach to Bifurcation in Lp on an Unbounded Symmetrical Domain.
A variational method to study the Zakharov equation.
A variational principle for complex boundary value problems.
About boundary terms in higher order theories
It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to the addition of boundary terms to the action, as it happens instead when the correct procedure is applied. Examples are considered to show how leaving derivatives of fields unconstrained affects the physical interpretation of the model. This is justified in particular...
About stability and regularization of ill-posed elliptic Cauchy problems: the case of C1,1 domains
This paper is devoted to a conditional stability estimate related to the ill-posed Cauchy problems for the Laplace's equation in domains with C1,1 boundary. It is an extension of an earlier result of [Phung, ESAIM: COCV9 (2003) 621–635] for domains of class C∞. Our estimate is established by using a Carleman estimate near the boundary in which the exponential weight depends on the distance function to the boundary. Furthermore, we prove that this stability estimate is nearly optimal and induces...
About the Morse Theory for Certain Variational Problems.
Abstract evolution equations on variable domains : an approach by minimizing movements
Active optimal control of the KdV equation using the variational iteration method.
An algorithm for hybrid regularizers based image restoration with Poisson noise
In this paper, a hybrid regularizers model for Poissonian image restoration is introduced. We study existence and uniqueness of minimizer for this model. To solve the resulting minimization problem, we employ the alternating minimization method with rigorous convergence guarantee. Numerical results demonstrate the efficiency and stability of the proposed method for suppressing Poisson noise.
An application of category theory to a class of the systems of the superquadratic wave equations.
An Elementary Partial Regularity Proof for Vector-Valued Obstacle Problems.
An elliptic equation with spike solutions concentrating at local minima of the Laplacian of the potential.