相关论文: A Variation on the Donsker-Varadhan Inequality for…

The present work is devoted to the study of a boundary value problem for second order linear differential equation set on singular cylindrical domain. This problem can be regarded via a natural change of variables as an elliptic abstract…

We compute the first Dirichlet eigenvalue of a geodesic ball in a rotationally symmetric model space in terms of the moment spectrum for the Brownian motion exit times from the ball. This expression implies an estimate as exact as you want…

This paper investigates the first Dirichlet eigenvalue for the $p$-Laplacian in Riemannian manifolds. Firstly, we establish a lower bound for this eigenvalue under the condition that the domain includes a specific function which fulfills…

In this paper, we investigate the well-posedness and the long-time asymptotic behavior for the initial-boundary value problem for multi-term time-fractional diffusion equations, where the time differentiation consists of a finite summation…

We investigate the diffusive motion of an overdamped classical particle in a 1D random potential using the mean first-passage time formalism and demonstrate the efficiency of this method in the investigation of the large-time dynamics of…

We consider a run-and-tumble particle on a half-line with an absorbing target at the origin. The particle has an internal velocity state that switches between two opposite values at Poisson-distributed times. The position of the particle…

In this paper in the cylindrical domain we consider a fractional elliptic operator with Dirichlet conditions. We prove, that the first eigenvalue of the fractional elliptic operator is minimised in a circular cylinder among all cylindrical…

We are interested in the spectrum of the Dirichlet Laplacian in thin broken strips with angle $\alpha$. Playing with symmetries, this leads us to investigate spectral problems for the Laplace operator with mixed boundary conditions in…

The first-order approach to boundary value problems for second-order elliptic equations in divergence form with transversally independent complex coefficients in the upper half-space rewrites the equation algebraically as a first-order…

We consider an elliptic operator in which the second-order term is very small in one direction. In this regime, we study the behaviour of the principal eigenfunction and of the principal eigenvalue. Our first result deals with the limit of…

We prove a sharp asymptotic formula for the mean exit time from a bounded domain $D\subset \mathbb R^d$ for the overdamped Langevin dynamics $$d X_t = -\nabla f(X_t) d t + \sqrt{2\ve} \ d B_t$$ when $\ve \to 0$ and in the case when $D$…

We consider a periodic-parabolic eigenvalue problem with a non-negative potential $\lambda m$ vanishing on a non-cylindrical domain $D_m$ satisfying conditions similar to those for the parabolic maximum principle. We show that the limit as…

We investigate the statistics of the local time $\mathcal{T} = \int_0^T \delta(x(t)) dt$ that a run and tumble particle (RTP) $x(t)$ in one dimension spends at the origin, with or without an external drift. By relating the local time to the…

Let $D\subset R^d$ be a bounded domain and let $\mathcal P(D)$ denote the space of probability measures on $D$. Consider a Brownian motion in $D$ which is killed at the boundary and which, while alive, jumps instantaneously according to a…

Let $\Omega\subset \mathbb R^2$ be a bounded planar domain, with piecewise smooth boundary $\partial \Omega$. For $\sigma>0$, we consider the Robin boundary value problem \[ -\Delta f =\lambda f, \qquad \frac{\partial f}{\partial n} +…

We investigate the effect of small diffusion on the principal eigenvalues of linear time-periodic parabolic operators with zero Neumann boundary conditions in one dimensional space. The asymptotic behaviors of the principal eigenvalues, as…

In this paper we prove a sharp lower bound for the first nontrivial Neumann eigenvalue $\mu_1(\Omega)$ for the $p$-Laplace operator in a Lipschitz, bounded domain $\Omega$ in $\R^n$. Our estimate does not require any convexity assumption on…

In this paper we extend classical criteria for determining lower bounds for the least point of the essential spectrum of second-order elliptic differential operators on domains $\Omega\subset\R^n$ allowing for degeneracy of the coefficients…

We prove a local Faber-Krahn inequality for solutions $u$ to the Dirichlet problem for $\Delta + V$ on an arbitrary domain $\Omega$ in $\mathbb{R}^n$. Suppose a solution $u$ assumes a global maximum at some point $x_0 \in \Omega$ and…

We consider a dynamical system described by the differential equation $\dot{Y}_t=-U'(Y_t)$ with a unique stable point at the origin. We perturb the system by the L\'evy noise of intensity $\varepsilon$ to obtain the stochastic differential…