We study variational problems involving the measure of level sets, or more precisely the push-forward of the Lebegue measure. This problem generalizes variational problems with finitely many (discrete) volume constraints. We obtain existence results for this general framework. Moreover, we show the surprising existence of asymmetric solutions to symmetric variational problems with this type of ...

We propose a numerical variational method for three-dimensional (3D) classical lattice models. We construct the variational state as a product of local tensors, and improve it by use of the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG) applied to 2D classical systems. Numerical efficiency of this approximation is inve...

In this work, the least squares weighted residual method is used to solve the two-dimensional (2D) elasticity problem of a rectangular plate of in-plane dimensions 2a 2b subjected to parabolic edge tensile loads applied at the two edges x = a. The problem is expressed using Beltrami–Michell stress formulation. Airy’s stress function method is applied to the stress compatibility equation, and th...

It is well known that the quasi variational inequalities are equivalent to the fixed point problems. We this equivalent alternative formulation to discuss the existence of a solution of quasi variational inequalities under some mild conditions. Since the quasi variational inequalities include variational inequalities, implicit complementarity problems and optimization problems as special cases,...

A global regularity theorem for stress fields which correspond to minimisers of convex and some special nonconvex variational problems is derived for Lipschitz-domains. In the first part it is assumed that the energy densities defining the variational problem are convex but not necessarily strictly convex and satisfy a convexity inequality. The regularity result for this case is derived with a ...

In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a so...

in this work, the blasius equation is studied. homotopy perturbation method (hpm) and homotopy analysis method (ham) are applied to obtain its solution. comparison with variational iteration method (vim) is made to highlight the significant features of employed methods and their capability of handling nonlinear problems. the outcome shows the success of (hpm) and (ham) for solving nonlinear pro...

In this paper, we address the problems of modeling the acoustic space generated by a full-spectrum sound source and using the learned model for the localization and separation of multiple sources that simultaneously emit sparse-spectrum sounds. We lay theoretical and methodological grounds in order to introduce the binaural manifold paradigm. We perform an in-depth study of the latent low-dimen...