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We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…
In this note we derive large-scale regularity properties of solutions to second-order linear elliptic equations with random coefficients on the half- space with homogeneous Neumann boundary data; it is a companion to arXiv:1604.02717 in…
We analyze the behavior of solutions of the Poisson equation with homogeneous Neumann boundary conditions in a two-dimensional thin domain which presents locally periodic oscillations at the boundary. The oscillations are such that both the…
In this paper, we are interested in the reiterated homogenization of linear elliptic equations of the form $-\frac{\partial}{\partial x_{i}} \left(a_{i j} \left(\frac{x}{\varepsilon}, \frac{x}{\varepsilon^{2}}\right) \frac{\partial…
The paper deals with homogenisation problems for high-contrast symmetric convolution-type operators with integrable kernels in media with a periodic microstructure. We adapt the two-scale convergence method to nonlocal convolution-type…
We consider an elliptic equation in a cone, endowed with (possibly inhomogeneous) Neumann conditions. The operator and the forcing terms can also allow non-Lipschitz singularities at the vertex of the cone. In this setting, we provide…
Motivated by experimental studies on the anomalous diffusion of biological populations, we introduce a nonlocal differential operator which can be interpreted as the spectral square root of the Laplacian in bounded domains with Neumann…
We prove localized energy estimates for the wave equation in domains with a strictly concave boundary when homogeneous Dirichlet or Neumann conditions are imposed. By restricting the solution to small, frequency dependent, space time…
The aim of this paper is to state and prove existence and uniqueness results for a general elliptic problem with homogeneous Neumann boundary conditions, often associated with image processing tasks like denoising. The novelty is that we…
For a second-order strongly elliptic differential operator on an exterior domain in R^n it is known from works of Birman and Solomiak that a change of the boundary condition from the Dirichlet condition to an elliptic Neumann or Robin…
For a linear, strictly elliptic second order differential operator in divergence form with bounded, measurable coefficients on a Lipschitz domain $\Omega$ we show that solutions of the corresponding elliptic problem with Robin and thus in…
We consider the nonlinear Neumann problem for fully nonlinear elliptic PDEs on a quadrant. We establish a comparison theorem for viscosity sub and supersolutions of the nonlinear Neumann problem. The crucial argument in the proof of the…
We study an inhomogeneous Neumann boundary value problem for functions of least gradient on bounded domains in metric spaces that are equipped with a doubling measure and support a Poincar\'e inequality. We show that solutions exist under…
This paper investigates the regularity of solutions and structural properties of the free boundary for a class of fourth-order elliptic problems with Neumann-type boundary conditions. The singular and degenerate elliptic operators studied…
We consider a boundary value problem for a general second order linear equation in a domain with a fine perforation. The latter is made by small cavities; both the shapes of the cavities and their distribution are arbitrary. The boundaries…
In this paper we propose a Local Orthogonal Decomposition method (LOD) for elliptic partial differential equations with inhomogeneous Dirichlet- and Neumann boundary conditions. For this purpose, we present new boundary correctors which…
We consider periodic homogenization with localized defects for semilinear elliptic equations and systems of the type $$ \nabla\cdot\Big(\Big(A(x/\varepsilon)+B(x/\varepsilon)\Big)\nabla u(x)+c(x,u(x)\Big)=d(x,u(x)) \mbox{ in } \Omega $$…
This paper is concerned with the study of theexistence/non-existence of the discrete spectrum of the Laplaceoperator on a domain of $\mathbb R ^3$ which consists in atwisted tube. This operator is defined by means of mixed…
We obtain conditions for the differentiability of weak solutions for a second-order uniformly elliptic equation in divergence form with a homogeneous co-normal boundary condition. The modulus of continuity for the coefficients is assumed to…
Continuous data assimilation addresses time-dependent problems with unknown initial conditions by incorporating observations of the solution into a nudging term. For the prototypical heat equation with variable conductivity and the Neumann…