We study a generalization of the fully overdamped Frenkel-Kontorova model in dimension n ≥ 1. This model describes the evolution of the position of each atom in a crystal, and is mathematically given by an infinite system of coupled first order ODEs. We prove that for a suitable rescaling of this model, the solution converges to the solution of a Peierls-Nabarro model, which is a coupled system...

We consider a convective-diffusive elliptic problem with Neumann boundary conditions: the presence of the convective term entails the non-coercivity of the continuous equation and, because of the boundary conditions, the equation has a kernel. We discretize this equation with finite volume techniques and in a general framework which allows to consider several treatments of the convective term: ...

In this article, we discuss a least-squares/fictitious domain method for the solution of linear elliptic boundary value problems with Robin boundary conditions. Let Ω and ω be two bounded domains of Rd such that ω⊂Ω. For a linear elliptic problem in Ω\ω with Robin boundary condition on the boundary γ of ω, our goal here is to develop a fictitious domain method where one solves a variant of the ...

In this paper we consider the following mathematical model: an elliptic boundary value problem, where the partial differential equation contains advection, diffusion, and deposition parts. A Monte Carlo (MC) method to solve this equation uses a local integral representation by the Green’s function and a random process called “Walks on Balls”(WOB). A new class of grid free MC algorithms for solv...

We discuss the problem of prescribing the mean curvature and conformal class as boundary data for Einstein metrics on 3-manifolds, in the context of natural elliptic boundary value problems for Riemannian metrics.

We obtain a global extension of the classical weak Harnack inequality which extends and quantifies Hopf–Oleinik boundary-point lemma, for uniformly elliptic equations in divergence form. Among consequences is boundary gradient estimate, due to Krylov well-studied non-divergence form equations, but completely novel framework. Another consequence new more general version lemma.

In this paper, we prove the existence of the solution for boundary value prob-lem(BVP) of fractional dierential equations of order q 2 (2; 3]. The Kras-noselskii's xed point theorem is applied to establish the results. In addition,we give an detailed example to demonstrate the main result.

In this paper, we prove the existence of the solution for boundary value prob-lem(BVP) of fractional dierential equations of order q 2 (2; 3]. The Kras-noselskii's xed point theorem is applied to establish the results. In addition,we give an detailed example to demonstrate the main result.