Related papers: Quantitative unique continuation for the heat equa…
The chiral phase transition of the quark sector of QCD is investigated within the Hamiltonian approach in Coulomb gauge. Finite temperature T is introduced by compactifying one spatial dimension, which makes all thermodynamical quantities…
The purpose of this article is to expose and further develop a simple yet surprisingly far-reaching framework for generating monotone quantities for positive solutions to linear heat equations in euclidean space. This framework is…
We consider the Cauchy problem posed in the whole space for the following nonlocal heat equation: u_t = J * u - u, where J is a symmetric continuous probability density. Depending on the tail of J, we give a rather complete picture of the…
We consider the quantitative uniqueness properties for a parabolic type equation $ u_t-\Delta u = w(x,t) \nabla u + v(x,t) u$, when $v \in L^{p_2}_{t} L^{p_1}_x$ and $w \in L^{q_2}_{t} L^{q_1}_x$, with a suitable range for exponents $p_1$,…
We investigate the H\"older continuity of solutions to stochastic partial differential equations of the form $\frac{\partial u}{\partial t}=\mathcal{L}u+\sigma(u)\dot{F}$, subject to a suitable initial condition. The noise term $\dot{F}$ is…
In this paper, we prove the H\"older continuity for solutions to the complex Monge-Amp\`ere equations on non-smooth pseudoconvex domains of plurisubharmonic type ${m}$.
In this paper, we are concerned with regularity of nonlocal stochastic partial differential equations of parabolic type. By using Companato estimates and Sobolev embedding theorem, we first show the H\"{o}lder continuity (locally in the…
In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone multivalued subdifferential boundary condition on a portion of the boundary…
In this note we analyse \emph{quantitative} approximation properties of a certain class of \emph{nonlocal} equations: Viewing the fractional heat equation as a model problem, which involves both \emph{local} and \emph{nonlocal}…
We study some thermodynamics quantities for the Klein-Gordon equation with a linear plus inverse-linear, scalar potential. We obtain the energy eigenvalues with the help of the quantization rule coming from the biconfluent Heun's equation.…
We consider a system of $d$ linear stochastic heat equations driven by an additive infinite-dimensional fractional Brownian noise on the unit circle $S^1$. We obtain sharp results on the H\"older continuity in time of the paths of the…
We present a new stochastic analysis for steady and transient one-dimensional heat conduction problem based on the homogenization approach. Thermal conductivity is assumed to be a random field K consisting of random variables of a total…
We establish the $L^2$-solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with H\"older-continuous diffusion coefficients, on bounded Lipschitz domains in $\mathbb{R}^n$. This is…
In this article we study the strong unique continuation property for solutions of higher order (variable coefficient) fractional Schr\"odinger operators. We deduce the strong unique continuation property in the presence of subcritical and…
The potential energy of a static charge distribution on a lattice is rigorously computed in the standard compact quantum electrodynamic model. The method used follows closely that of Weyl for ordinary quantum electrodynamics in continuous…
We discuss the application of techniques of quantum estimation theory and quantum metrology to thermometry. The ultimate limit to the precision at which the temperature of a system at thermal equilibrium can be determined is related to the…
We present a family of integral equation-based solvers for the linear or semilinear heat equation in complicated moving (or stationary) geometries. This approach has significant advantages over more standard finite element or finite…
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…
In this paper, we prove a differential Harnack inequality for positive solutions of time-dependent heat equations with potentials. We also prove a gradient estimate for the positive solution of the time-dependent heat equation.
Existence, uniqueness and stability of solutions is studied for a set of nonlinear fixed point equations which define self-consistent hydrostatic equilibria of a classical continuum fluid that is confined inside a container and in contact…