Variation of constants formula for functional parabolic partial differential equations.
Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket
Under an appropriate oscillating behaviour either at zero or at infinity of the nonlinear term, the existence of a sequence of weak solutions for an eigenvalue Dirichlet problem on the Sierpiński gasket is proved. Our approach is based on variational methods and on some analytic and geometrical properties of the Sierpiński fractal. The abstract results are illustrated by explicit examples.
Variational analysis for the Black and Scholes equation with stochastic volatility
We propose a variational analysis for a Black and Scholes equation with stochastic volatility. This equation gives the price of a European option as a function of the time, of the price of the underlying asset and of the volatility when the volatility is a function of a mean reverting Orstein-Uhlenbeck process, possibly correlated with the underlying asset. The variational analysis involves weighted Sobolev spaces. It enables to prove qualitative properties of the solution, namely a maximum principle...
Variational Analysis for the Black and Scholes Equation with Stochastic Volatility
We propose a variational analysis for a Black and Scholes equation with stochastic volatility. This equation gives the price of a European option as a function of the time, of the price of the underlying asset and of the volatility when the volatility is a function of a mean reverting Orstein-Uhlenbeck process, possibly correlated with the underlying asset. The variational analysis involves weighted Sobolev spaces. It enables to prove qualitative properties of the solution, namely a maximum principle...
Variational and boundary value problems for differential equations with deviating argument
Variational and topological methods for Dirichlet problems with -Laplacian.
Variational and topological methods for operator equations involving duality mappings on Orlicz-Sobolev spaces.
Variational approach to dynamics of bright solitons in lossy optical fibers.
Variational approach to impulsive differential equations with Dirichlet boundary conditions.
Variational approximation methods for eigenvalues. Convergence theorems
Variational characterization of eigenvalues of a non-symmetric eigenvalue problem governing elastoacoustic vibrations
Small amplitude vibrations of an elastic structure completely filled by a fluid are considered. Describing the structure by displacements and the fluid by its pressure field one arrives at a non-selfadjoint eigenvalue problem. Taking advantage of a Rayleigh functional we prove that its eigenvalues can be characterized by variational principles of Rayleigh, minmax and maxmin type.
Variational characterization of interior interfaces in phase transition models on convex plane domains.
Variational convergence of nonlinear diffusion equations: applications to concentrated capacity problems with change of phase
We study a variational formulation for a Stefan problem in two adjoining bodies, when the heat conductivity of one of them becomes infinitely large. We study the «concentrated capacity» model arising in the limit, and we justify it by an asymptotic analysis, which is developed in the general framework of the abstract evolution equations of monotone type.
Variational data assimilation for discrete Burgers equation.
Variational Framework for Assessment of the Left Ventricle Motion
Impairment of left ventricular contractility due to cardiovascular diseases is reflected in left ventricle (LV) motion patterns. An abnormal change of torsion or long axis shortening LV values can help with the diagnosis and follow-up of LV dysfunction. Tagged Magnetic Resonance (TMR) is a widely spread medical imaging modality that allows estimation of the myocardial tissue local deformation. In this work, we introduce a novel variational framework for extracting the left ventricle dynamics from...
Variational inequalities and rearrangements
We give comparison results for solutions of variational inequalities, related to general elliptic second order operators, involving solutions of symmetrized problems, using Schwarz spherical symmetrization.
Variational inequalities for energy functionals with nonstandard growth conditions.
Variational inequalities for vector-valued functions.
Variational inequalities of strongly nonlinear elliptic operators of infinite order.
Variational iteration method for initial and boundary value problems using He's polynomials.