Related papers: On Positive Harmonic Functions in Cones and Cylind…

In this paper we generalise a useful result due to J. Mierczynski which states that for a strictly cooperative system on the positive orthant, with increasing first integral, all bounded orbits are convergent. Moreover any equilibrium…

We establish the existence of positive solutions to a general class of overdetermined semilinear elliptic boundary problems on suitable bounded open sets $\Omega\subset\mathbb{R}^n$. Specifically, for $n\leq 4$ and under mild technical…

We consider rotating black hole solutions in five-dimensional Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant and a generic value of the Chern-Simons coupling constant $\lambda$. Using both analytical and…

Given two elliptic operators L and M in nondivergence form, with coefficients A_L(x), A_M(x) and drift terms b_L(x), b_M(x), respectively, satisfying a Carleson measure disagreement condition in a Lipschitz domain Omega in R^{n+1}, then…

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in…

Given a bounded Lipschitz domain $\omega\subset\mathbb{R}^{d-1}$ and a lower semicontinuous function $W:\mathbb{R}^N\to\mathbb{R}_+\cup\{+\infty\}$ that vanishes on a finite set and that is bounded from below by a positive constant at…

Let $\omega\subset\mathbb{R}^n$ be a bounded domain with Lipschitz boundary. For $\varepsilon>0$ and $n\in\mathbb{N}$ consider the infinite cone $\Omega_{\varepsilon}:=\big\{(x_1,x')\in (0,\infty)\times\mathbb{R}^n: x'\in\varepsilon…

In this paper, we give a few results on the local behavior of harmonic functions on the Sierpinski triangle - more precisely, of their restriction to a side of the triangle. First we present a general formula that gives the H\"older…

In this paper, we study the infinity harmonic functions with linear growth rate at infinity defined on exterior domains. We show that such functions must be asymptotic to planes or cones at infinity. We also establish the solvability of…

We study an overdetermined eigenvalue problem for domains $\Omega$ contained in the half-cylinder $\Sigma=\omega \times (0, +\infty)$, based on a bounded regular domain $\omega \subset \mathbb{R}^{N-1}$. It is easy to see that in any…

Let $\alpha\in (0, 1]$, $\beta\in [0, n)$ and $T_{\Omega,\beta}$ be a singular or fractional integral operator with homogeneous kernel $\Omega$. In this article, a CMO type space ${\rm CMO}_\alpha(\mathbb R^n)$ is introduced and studied. In…

We characterize the set of positive harmonic functions with Dirichlet boundary conditions in unbounded domains which are union of several different chambers. We analyze the asymptotic behavior of the solutions in connection with the changes…

In this note, we extend the well-known theorems of M. Riesz and Zygmund on conjugate functions as follows. Let $\Omega$ be a domain in $\mathbb C^n$. Suppose that $f=u+iv\in \mathcal O(\Omega)$ satisfies $v(z_0)=0$ for some $z_0\in \Omega$.…

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…

Non-relativistic conformally invariant systems in a rotating cosmic string (conical) spacetime are analyzed at the classical and quantum levels by means of the gravitoelectromagnetic interpretation of the background. Solutions of the…

In this paper, we provide an affirmative answer to the {\it conjecture A} for bounded simple rotationally symmetric domains $\Omega\subset \mathbb{R}^n(n\geq 3)$ along $x_n$ axis. Precisely, we use a new simple argument to study the…

Let $\Omega \subset \mathbb{R}^{n+1}$ be an open set whose boundary may be composed of pieces of different dimensions. Assume that $\Omega$ satisfies the quantitative openness and connectedness, and there exist doubling measures $m$ on…

The Hardy-Littlewood maximal function $\mathcal{M}$ and the trigonometric function $\sin{x}$ are two central objects in harmonic analysis. We prove that $\mathcal{M}$ characterizes $\sin{x}$ in the following way: let $f \in…

The main thrust of our current work is to exploit very specific characteristics of a given problem in order to acquire improved compactness for supercritical problems and to prove existence of new types of solutions. To this end, we shall…

In the junction $\Omega$ of several semi-infinite cylindrical waveguides we consider the Dirichlet Laplacian whose continuous spectrum is the ray $[\lambda_\dagger, +\infty)$ with a positive cut-off value $\lambda_\dagger$. We give two…