Narrow Results

We study the problem of minimizing the $L^p$ norm of the curl of vector fields in a three-dimensional, bounded multi-connected domain with a prescribed tangential component on the boundary. We then prove the existence of minimizers and estimate them.

The purpose of this paper is to provide a general overview of a curvature functional in Finsler geometry and use its information to introduce the gradient flow on Finsler manifolds. For this purpose, we first make some differentiable structures on a domain of Finslerian functionals. Then by means of the global inner product and the Berger–Ebin Theorem, we make some decomposition for the tangent space of the manifold of all Finslerian metrics. Next, we study Akbar–Zadeh curvature functional as a Finslerian functional and we find the critical points of this functional in the pointwise conformal metric direction. Through this way, we introduce a gradient flow on compact Finsler manifold. Finally, we compare this new flow with introducing Ricci flow in Finsler geometry.

We present the evolutionary algorithm that evolves the population of numerical solutions of the variational problem. The evolved solutions are model-independent, smooth, can have a predefined shape (if needed), and satisfy boundary or any other additional conditions (if imposed). To exemplify the performance of the proposed algorithm, we show how to solve the variational problem of searching for the spatially modulated distribution of the field of order parameter that gives a minimum to the Landau-type thermodynamic potential in the theory of ferroelectrics with incommensurate phases.

New conservation laws associated to a variational problem are stated, to this aim the Poincaré–Cartan form assumed to be an essential element in the multisymplectic description of Classical Field Theories.

A free boundary problem that arises from the physical phenomenon of "peeling a thin tape from a domain" is treated. In this phenomenon, the movement of the tape is governed by a hyperbolic equation and is affected by the peeling front. We are interested in the behavior of the peeling front, especially, the phenomenon of self-excitation vibration. In the present paper, a mathematical model of this phenomenon is proposed. The cause of this vibration is discussed in terms of adhesion.

The purpose of this paper is to investigate the existence of a weak solution to a non-local elliptic system, driven by the fractional $m(\cdot )$-Laplacian operator in fractional Orlicz–Sobolev space that may be non-reflexive. The non-reflexive case occurs when the Orlicz function $\overline{M}$ does not verify the ${\mathrm{\Delta }}_2$-condition.

A class of positive Azéma–Yor martingales was first introduced in the option pricing context by Peter Carr (2014). In this paper, we present a rigorous study of the short maturity asymptotics for Asian, upper barrier, lower barrier and European options with continuous-time averaging, under the assumption that the underlying asset follows a Azéma–Yor martingale.

A one-dimensional free boundary problem of hyperbolic type will be analyzed. This problem arises from the physical model "Peel a thin film from a domain". The local solutions have been already given for our problem. However, it is not sure that the solutions can be extended globally. In this note, by applying an iteration method, it will be shown that time-global solutions exist.