Existence and qualitative properties of isoperimetric sets in periodic media
نویسندگان
چکیده
We review and extend here some recent results on the existence of minimal surfaces and isoperimetric sets in non homogeneous and anisotropic periodic media. We also describe the qualitative properties of the homogenized surface tension, also known as stable norm (or minimal action) in Weak KAM theory. In particular we investigate its strict convexity and differentiability properties.
منابع مشابه
The Isoperimetric Problem in the Grushin Space R With Density |x|
In this paper we study the isoperimetric problem in a class of x-spherically symmetric sets in the Grushin space R with density |x|, p > −h + 1. First we prove the existence of weighted isoperimetric sets. Then we deduce that, up to a vertical translation, a dilation and a negligible set, the weighted isoperimetric set is only of the form { (x, y) ∈ R : |y| < ∫ π 2 arcsin |x| sin (t)dt, |x| < 1...
متن کاملTransmission Properties of the Periodic Structures Based on Graphene Nonlinear Optical Conductivity in a Terahertz Field
By developing the terahertz (THz) technology, in addition to generators and detectors of THz waves, the existence of some tools such as modulators and filters are needed. THz filters are important tools for various applications in the field of chemical and biological sensors. Linear and nonlinear optical properties of the graphene have attracted lots of attention. In fact graphene exhibits vari...
متن کاملTransition fronts for periodic bistable reaction-diffusion equations
This paper is concerned with the existence and qualitative properties of transition fronts for spatially periodic reaction-diffusion equations with bistable nonlinearities. The notion of transition fronts connecting two stable steady states generalizes the standard notion of pulsating fronts. In this paper, we prove that the time-global solutions in the class of transition fronts share some com...
متن کامل-spectral gaps for time discrete reversible Markov chains
In this paper we study the spectral properties of Markov-operator on L -spaces. Lawler and Sokal (Trans. Amer. Math. Soc., 1988, 309, pp. 557-580) used isoperimetric constants for discrete and continuous time Markov chains to obtain a spectral gap at 1. For time discrete Markov chains this does not exclude periodic behavior. We define a new constant measuring the distance from periodicity and g...
متن کاملQualitative Properties and Existence of Solutions for a Generalized Fisher-like Equation
This paper is devoted to the study of an eigenvalue second order differential equation, supplied with homogenous Dirichlet conditions and set on the real line. In the linear case, the equation arises in the study of a reaction-diffusion system involved in disease propagation throughout a given population. Under some relations upon the real parameters and coefficients, we present some existence ...
متن کامل