Related papers: Sharp two-sided Green function estimates for Diric…
We establish existence and pointwise estimates of fundamental solutions and Green's matrices for divergence form, second order strongly elliptic systems in a domain $\Omega \subseteq \mathbb{R}^n$, $n \geq 3$, under the assumption that…
We study infinite tree and ultrametric matrices, and their action on the boundary of the tree. For each tree matrix we show the existence of a symmetric random walk associated to it and we study its Green potential. We provide a…
Let $D$ be an open set of $\mathbb{R}^d$, $\alpha\in (0, 2)$ and let $\mathcal{L}_{\alpha}^D$ be the generator of the censored $\alpha$-stable process in $D$. In this paper, we establish sharp two-sided heat kernel estimates for…
The boundary Green's function (bGF) approach has been established as a powerful theoretical technique for computing the transport properties of tunnel-coupled hybrid nanowire devices. Such nanowires may exhibit topologically nontrivial…
We consider a countable tree $T$, possibly having vertices with infinite degree, and an arbitrary stochastic nearest neighbour transition operator $P$. We provide a boundary integral representation for general eigenfunctions of $P$ with…
We prove sharp L^2 boundary decay estimates for the eigenfunctions of certain second order elliptic operators acting in a bounded region, and of their first order space derivatives, using only the Hardy inequality. We then deduce bounds on…
There is a unique Lorentz-violating modification of the Maxwell theory of photons, which maintains gauge invariance, CPT, and renormalizability. Restricting the modified-Maxwell theory to the isotropic sector and adding a standard…
We consider a random, uniformly elliptic coefficient field $a(x)$ on the $d$-dimensional integer lattice $\mathbb{Z}^d$. We are interested in the spatial decay of the quenched elliptic Green function $G(a;x,y)$. Next to stationarity, we…
In convex bounded domains in R^n with n >= 3, we establish interior pointwise upper bounds for the Dirichlet Green's function of elliptic operators in the unit ball B(0,1) in R^n, n >= 3, whose principal part is the Laplacian and which…
This paper provides decay bounds for Green matrices and generalized eigenvectors of block Jacobi operators when the real part of the spectral parameter lies in a bounded gap of the operator's essential spectrum. The case of the spectral…
Functional Analysis of Variance (FANOVA) from Hilbert-valued correlated data with spatial rectangular or circular supports is analyzed, when Dirichlet conditions are assumed on the boundary. Specifically, a Hilbert-valued fixed effect model…
Let $\alpha(x)$ be a measurable function taking values in $ [\alpha_1,\alpha_2]$ for $0<\A_1\le \A_2<2$, and $\kappa(x,z)$ be a positive measurable function that is symmetric in $z$ and bounded between two positive constants. Under a…
We show that if either the process is strong Feller and the boundary point is probabilistically regular for the stopping set, or the process is strong Markov and the boundary point is probabilistically regular for the interior of the…
Structure and coordinate dependence of the reflected wave, as well as boundary conditions for quasi-particles of graphene and the two dimensional electron gas in sheets with abrupt lattice edges are obtained and analyzed by the Green's…
We prove a \(\Gamma\)-convergence result for a diffeomorphism-natural discrete MDL-type functional to the Einstein-Hilbert action with the Gibbons-Hawking-York boundary term. On boundary-fitted, shape-regular meshes we establish interior…
The quantum correlations of $N$ noninteracting spinless fermions in their ground state can be expressed in terms of a two-point function called the kernel. Here we develop a general and compact method for computing the kernel in a general…
The Brownian motion over the space of fluid velocity configurations driven by the hydrodynamical equations is considered. The Green function is computed in the form of an asymptotic series close to the standard diffusion kernel. The high…
In this article, we consider a nabla fractional boundary value problem with general boundary conditions. Brackins \& Peterson \cite{Br} gave an explicit expression for the corresponding Green's function. Here, we show that this Green's…
We prove a number of \textit{a priori} estimates for weak solutions of elliptic equations or systems with vertically independent coefficients in the upper-half space. These estimates are designed towards applications to boundary value…
In this paper, we study sharp two-sided heat kernel estimates for a large class of symmetric reflected diffusions with jumps on the closure of an inner uniform domain $D$ in a length metric space. The length metric is the intrinsic metric…