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Weighted Poincaré Inequalities and Degenerate Elliptic and Parabolic Problems: An Approach via the Distance Function
We obtain weighted Poincaré inequalities in bounded domains, where the weight is given by a symmetric nonnegative definite matrix, which can...
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The exact solutions of Fokas-Lenells equation based on Jacobi elliptic function expansion method
The Fokas-Lenells (FL) equation, which is rich in physical property in soliton theory as well as optical fiber, is a generalization of the...
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Novel Solitary and Periodic Wave Solutions of the Benjamin–Bona–Mahony Equation via the Weierstrass Elliptic Function Method
This paper presents the Weierstrass elliptic function solutions of the Riccati equation and four conversion formulas for converting the Weierstrass...
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On Twisted Elliptic Genera
We study the twisted elliptic genera associated to the BPS strings in the twisted circle compactification of 6d (1,0) SCFTs. Such objects can arise...
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Applications of Jacobi’s Elliptic Functions
In the previous chapter we defined Jacobi’s elliptic function sn as the inverse function of the incomplete elliptic integral of the first kind,...
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On the Smoothness of a Function at the Convergence Point of Its Spectral Expansion Associated with B-Elliptic Operators
AbstractIn this paper, the necessary conditions for summability of spectral expansions in eigenfunctions of the Bessel type singular elliptic...
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Inversion formulas for the j-function around elliptic points
Recently, Hong, Mertens, Ono, and Zhang [
8 ] proved a conjecture of Căldăraru, He, and Huang [4 ] that expresses the Taylor series of the modular j -func... -
Elliptic Curves over the Rationals
This chapter covers prerequisites on elliptic curves over $$\mathbb...
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Properties of some elliptic Hill’s potentials
We study Hill’s differential equation with potential expressed by elliptic functions which arises in some problems of physics and mathematics....
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Approximation of Zeros of Generalized Hermite Polynomials by Modulated Elliptic Function
Distribution of zeros of polynomials constitute a classic analytic problem. In the paper, a distribution of zeroes to generalized Hermite polynomials H
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Abel’s Approach to Elliptic Integrals
The theory of elliptic integrals and functions was a major research topic during the nineteenth century. Great mathematicians such as Euler,...
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Asymptotics of Solution Curves of Kirchhoff Type Elliptic Equations with Logarithmic Kirchhoff Function
We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with logarithmic Kirchhoff function. We establish the precise asymptotic...
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Elliptic groups and rings
As it is well known, one can define an abelian group on the points of an elliptic curve, using the so called chord–tangent law (Husemöller in...
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Classification of Elliptic Integrals
It is natural to call the former an elliptic integral, but why call the latter ‘elliptic’, even though the curve is not an ellipse? In fact, today...
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Elliptic Biquaternionic Sequence with Vietoris’ Numbers as Its Components
In this study, we introduce an elliptic biquaternionic sequence with Vietoris’ numbers as its components and discuss some of its properties. Also,...
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On an Efficient Solution of the Dirichlet Problem for Properly Elliptic Equation in the Elliptic Domain
AbstractThe fourth-order properly elliptic equation with multiple root is considered in the elliptic domain. The conditions, necessary and sufficient...
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Nonuniformly elliptic Schauder theory
Local Schauder theory holds in the nonuniformly elliptic setting. Specifically, first derivatives of solutions to nonuniformly elliptic problems are...
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Elliptic Curves Induced by Diophantine Triples
This chapter introduces elliptic curves induced by Diophantine triples and discusses their properties and applications. One of the main applications...