High-Resolution Color Image Reconstruction with Neumann Boundary Conditions

This paper studies the application of preconditioned conjugate gradient methods in high-resolution color image reconstruction problems. The high-resolution color images are reconstructed from multiple undersampled, shifted, degraded color frames with subpixel displacements. The resulting degradation matrices are spatially variant. To capture the changes of reflectivity across color channels, the weighted H ₁ regularization functional is used in the Tikhonov regularization. The Neumann boundary condition is also employed to reduce the boundary artifacts. The preconditioners are derived by taking the cosine transform approximation of the degradation matrices. Numerical examples are given to illustrate the fast convergence of the preconditioned conjugate gradient method.     

Estimates of Heat Kernels with Neumann Boundary Conditions

In this paper, we obtain two-sided estimates on the heat kernels for elliptic operators with singular coefficients equipped with mixed boundary conditions.     

Three Classes of Reaction-Diffusion Systems with Neumann Boundary Condition

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Convergence of Discrete Green Functions with Neumann Boundary Conditions

In this article we prove convergence of Green functions with Neumann boundary conditions for the random walk to their continuous counterparts. Our methods rely on local central limit theorems for convergence of random walks on discretizations of smooth domains to Reflected Brownian motion.     

Principal Eigenvalues for Isaacs Operators with Neumann Boundary Conditions

In this paper we show the existence of two principal eigenvalues associated to general non-convex fully nonlinear elliptic operators with Neumann boundary conditions in a bounded C ² domain. We study these objects and we establish some of their basic properties. Finally, Lipschitz regularity, uniqueness and existence results for the solution of the Neumann problem are given.      

Quenching Time for a Semilinear Heat Equation with a Nonlinear Neumann Boundary Condition

In this paper we consider the finite time quenching behavior of solutions to a semilinear heat equation with a nonlinear Neumann boundary condition. Firstly, we establish conditions on nonlinear source and boundary to guarantee that the solution doesn＇t quench for all time. Secondly, we give sufficient conditions on data such that the solution quenches in finite time, and derive an upper bound of quenching time. Thirdly, undermore restrictive conditions, we obtain a lower bound of quenching time. Finally, we give the exact bounds of quenching time of a special example.     

具Neumann边界条件的拟线性椭圆方程组的多解存在性

通过运用Ricceri的一个三临界点定理，得到了一类具变分结构的拟线性椭圆方程组的多解的存在性．     

齐次Neumann边界条件下反应扩散方程的指数吸引子

利用构造挤压性的方法,讨论了齐次Neumann边界条件下反应扩散方程u_t-△u+λu=f(u)+β在H_(0¹)(Ω)中的指数吸引子的存在性.     

Heat Content Asymptotics with Inhomogeneous Neumann and Dirichlet Boundary Conditions

Let M be a compact manifold with smooth boundary. We establish the existence of an asymptotic expansion for the heat content asymptotics of M with inhomogeneous Neumann and Dirichlet boundary conditions. We prove all the coefficients are locally determined and determine the first several terms in the asymptotic expansion.     

An Upper Estimate for a Heat Kernel With Neumann Boundary Condition

Using an upper solution we obtain a bound from above for theheat kernel (x,y,t) for a region which is star-shaped withrespect to one of the points, say y. The estimate is for theNeumann problem and holds for short times. The form of the boundis moreover, for x\Y(y), Here Y(y) is a closed subset of R^Nwith measure zero, d(x,y) is the minimum distance between xand y via the boundary :d(x,y) = inf_Z(|x-z| + |y-z|), and f(.,y)is a positive function, continuous away from Y, and equal tounity on .     

On the Stability of a SEIR Reaction Diffusion Model for Infections Under Neumann Boundary Conditions

This paper deals with a reaction-diffusion SEIR model for infections under homogeneous Neumann boundary conditions. The longtime behaviour of the solutions is analyzed and, in particular, absorbing sets in the phase space are determined. By using a peculiar Lyapunov function, the nonlinear asymptotic stability of endemic equilibrium is investigated.     

A Time-Dependent Strange Term Arising in Homogenization of an Elliptic Problem with Rapidly Alternating Neumann and Dynamic Boundary Conditions Specified at the Domain Boundary: The Critical Case

Doklady Mathematics - A strange term arising in the homogenization of elliptic (and parabolic) equations with dynamic boundary conditions given on some boundary parts of critical size is...     

Finite-Element Approximation of Elliptic Equations with a Neumann or Robin Condition on a Curved Boundary

This paper considers a finite-element approximation of a second-orderself adjoint elliptic equation in a region Rⁿ (with n=2 or 3)having a curved boundary on which a Neumann or Robin conditionis prescribed. If the finite-element space defined over , a union of elements, has approximation power h^kin the L² norm, and if the region of integration is approximatedby ^h with dist (, ^h)Ch^k, then it is shown that one retains optimalrates of convergence for the error in the H¹ and L² norms, whetherQ^h is fitted or unfitted , provided that the numerical integration scheme has sufficientaccuracy.     

Neumann Problem of Quasilinear Elliptic Equations with Limit Nonlinearity in Boundary Condition

This paper is concerned with the existence of solutions to the equation D_j(a^{ij}(x,u)D_i,u)-frac{1}{2}D_sa^{ij}(x,u)D_iuD_ju + λ u = 0 on a bounded domain under the Neumann boundary condition a{ij}(x,u)D_iuϒ_j = lul^{frac{2}{n-2}}u.     

Minimization of the Principal Eigenvalue Under Neumann Boundary Conditions

We investigate the minimization of the principal eigenvalue of the Laplacian under Neumann boundary conditions in case the weight has indefinite sign and varies in a class of rearrangements. Biologically, this minimization problem is motivated by the question of determining the most convenient spatial arrangement of favorable and unfavorable resources for a species to survive. The question may have practical importance in the context of reserve design.