Related papers: Dependence of the layer heat potentials upon suppo…
This paper is divided into three parts. The first part focuses on periodic layer heat potentials, demonstrating their smooth dependence on regular perturbations of the support of integration. In the second part, we present an application of…
The heat kernel coefficients $H_k$ to the Schr\"odinger operator with a matrix potential are investigated. We present algorithms and explicit expressions for the Taylor coefficients of the $H_k$. Special terms are discussed, and for the…
Let us consider a time-dependent differential operator quadratic with respect to the phase variables. Let us consider a multiplication operator defined with the help of a "small" matrix-valued function. Under suitable conditions, we give an…
In this note we show the optimal gradient estimate for heat kernels of stable-like operators by providing a counterexample.
In this work we establish some new estimates for layer potentials of the acoustic wave equation in the time domain, and for their associated retarded integral operators. These estimates are proven using time-domain estimates based on theory…
We consider a family of integral operators which appears when analyzing layered equilibria and front dynamics of a phase kinetics equation with a conservation law. We study the spectra of these operators in $L^2$ and derive a lower bound…
We consider the volume potential associated with the heat operator and we prove a mapping property in the space of distributions which are the time derivative of H\"older continuous functions. As an application we solve the Dirichlet and…
We study the effect of regular and singular domain perturbations on layer potential operators for the Laplace equation. First, we consider layer potentials supported on a diffeomorphic image $\phi(\partial\Omega)$ of a reference set…
We prove that the double layer potential operator and the gradient of the single layer potential operator are L_2 bounded for general second order divergence form systems. As compared to earlier results, our proof shows that the bounds for…
We introduce the phase model on a lattice and solve it using the algebraic Bethe ansatz. Time-dependent temperature correlation functions of phase operators and the "darkness formation probability" are calculated in the thermodynamical…
We give local in time sharp two sided estimates of the heat kernel associated with the relativistic stable operator perturbed by a critical (Hardy) potential.
Let $d\ge1$ and $0<\alpha<2$. Consider the integro-differential operator \[ \mathcal{L}f(x) =\int_{\mathbb{R}^{d}\backslash\{0\}}\left[f(x+h)-f(x)-\chi_{\alpha}(h)\nabla f(x)\cdot…
We study certain functions arising in the context of the calculation of correlation functions of the XXZ spin chain and of integrable field theories related with various scaling limits of the underlying six-vertex model. We show that…
Coherent quantum oscillators are basic physical systems both in quantum statistical physics and quantum thermodynamics. Their realizations in lab often involve solid-state devices sensitive to changes in ambient temperature. We represent…
By making use of the potentials of the heat conduction equation the integral equations are derived which determine the heat kernel for the Laplace operator $-a^2\Delta$ in the case of compound media. In each of the media the parameter $a^2$…
This article characterizes phase transitions in temperature within a specific space of H\"older continuous potentials, distinguished by their regularity and asymptotic behavior at zero. We also characterize the phase transitions in…
We introduce and study new invariants associated with Laplace type elliptic partial differential operators on manifolds. These invariants are constructed by using the off-diagonal heat kernel; they are not pure spectral invariants, that is,…
We prove the validity of regularizing properties of the boundary integral operator corresponding to the double layer potential associated to the fundamental solution of a {\em nonhomogeneous} second order elliptic differential operator with…
In this paper, we review the construction of periodic fundamental solutions and periodic layer potentials for various differential operators. Specifically, we focus on the Laplace equation, the Helmholtz equation, the Lam\'e system, and the…
We propose solar-shaped thermal concentrators designed with orthoradial layers and obtained in practice through the homogenization of an ideal thermal concentrator. Considering the spectral regime of the heat equation, we quantitatively…