Related papers: Variation formulas for principal functions (II) Ap…

We compute, for cosmological backgrounds, the $O(d,d;\mathbb{R})$ invariant beta functions for the sigma model of the bosonic string at two loops. This yields an independent first-principle derivation of the order $\alpha'$ corrections to…

Let \(\mathbb D\) denote the unit disc in \(\mathbb C\). For a domain \(D\subset\mathbb C\) and a point \(p\in D\), let \(M_D(p)\) denote the supremum of \(\|df_0\|\) over all harmonic maps \(f:\mathbb D\to D\) with \(f(0)=p\) whose…

Let $D$ be a smoothly bounded pseudoconvex domain in $\mathbf C^n$, $n > 1$. Using the Robin function $\La(p)$ that arises from the Green function $G(z, p)$ for $D$ with pole at $p \in D$ associated with the standard sum-of-squares…

The wave functions of a quantum isotropic harmonic oscillator in N-space modified by barriers at the coordinate hyperplanes can be expressed in terms of certain generalized spherical harmonics. These are associated with a product-type…

In the explicit formula for the signed mock theta functions $\Phi^{(-)[m,s]}$ obtained from the coroot lattice of $D(2,1;a)$, functions with indefinite quadratic forms naturally take place. We compute their modular transformation properties…

We investigate properties of ($\alpha,\beta$)-harmonic functions. First, we discuss the coefficient estimates for ($\alpha,\beta$)-harmonic functions. In particular, we obtain Heinz's inequality for ($\alpha,\beta$)-harmonic functions,…

This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…

We study from an algebraic point of view the question of extending an action of a group \(\Gamma\) on a commutative domain \(R\) to a formal pseudodifferential operator ring \(B=R(\!(x\,;\,d)\!)\) with coefficients in \(R\), as well as to…

This work concerns the study of the subdifferential of the integral functional $$ E_f(x)=\int_{T} f(t,x)d\mu(t), $$ where $f$ is a (not necessarily convex) normal integrand, $({T},\mathcal{A},\mu)$ is a $\sigma$-finite measure space, while…

Let ${\mathcal S^0}(H_{\gamma})$ denote the class of all univalent, harmonic, sense-preserving and normalized mappings $f$ of the unit disk $\ID$ onto the slanted half-plane $H_\gamma :=\{w:\,{\rm Re\,}(e^{i\gamma}w) >-1/2\}$ with an…

We derive explicit expressions for a family of radially symmetric, non-differentiable, Spartan covariance functions in $\mathbb{R}^2$ that involve the modified Bessel function of the second kind. In addition to the characteristic length and…

We study harmonic maps from Riemannian manifolds into arbitrary non-positively curved and CAT(-1) metric spaces. First we discuss the domain variation formula with special emphasis on the error terms. Expanding higher order terms of this…

Recent work has proposed a method for imposing T-duality on the metric, $B$-field, and dilaton of the classical effective action of string theory without using Kaluza-Klein reduction. Specifically, the $D$-dimensional effective action…

In the present note, we examine the behavior of some homo\-thecy-invariant differentiation basis of rectangles in the plane satisfying the following requirement: for a given rectangle to belong to the basis, the ratio of the largest of its…

In this paper, we focus on the sub-wavelength resonances in two-dimensional elastic media characterized by high contrasts in both Lam\'e parameters and density. Our contributions are fourfold. First, it is proved that the operator…

A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a…

Let a function $u(x,y)$ be harmonic in the domain $$ D\times V_r=D\times \{y\in \mathbb{R}^m: |y|<r\}\subset \mathbb{R}^n\times \mathbb{R}^m $$ and for each fixed point $x^0$ from some a set $E\subset D$, %which is not embedded in countable…

Let $T$ be a self-adjoint operator in a Hilbert space $H$ with domain $\mathcal D(T)$. Assume that the spectrum of $T$ is confined in the union of disjoint intervals $\Delta_k =[\alpha_{2k-1},\alpha_{2k}]$, $k\in \mathbb{Z}$, and $$…

We derive a variational formulation for the scalar wave equation in the second-order formulation on bounded Lipschitz domains and homogeneous initial conditions. We investigate a variational framework in a bounded space-time cylinder $Q$…

We prove the existence of a continuous $BV$ minimizer with $C^{0}$ boundary value for the $p$-area (pseudohermitian or horizontal area) in a parabolically convex bounded domain. We extend the domain of the area functional from $BV$…