Equivalence between the local boundedness property for parabolic Neumann BVP’s and the gaussian bound for their corresponding Green functions

Local boundedness property for parabolic BVP’s and the gaussian upper bound for their Green functions

Gaussian Type Bounds for the Neumann-green Function of a General Parabolic Operator

Based on the fact that the Neumann-Green function can be constructed as a perturbation of the fundamental solution by a single-layer potential, we establish a gaussian lower bound and a gaussian type upper bound for the Neumann-Green function for a general parabolic operator. We build our analysis on old tools coming from the construction of a fundamental solution of a general parabolic operato...

A MIXED PARABOLIC WITH A NON-LOCAL AND GLOBAL LINEAR CONDITIONS

Krein [1] mentioned that for each PD equation we have two extreme operators, one is the minimal in which solution and its derivatives on the boundary are zero, the other one is the maximal operator in which there is no prescribed boundary conditions. They claim it is not possible to have a related boundary value problem for an arbitrarily chosen operator in between. They have only considered lo...

Riesz Transform, Gaussian Bounds and the Method of Wave Equation

For an abstract self-adjoint operator L and a local operator A we study the boundedness of the Riesz transform AL on L for some α > 0. A very simple proof of the obtained result is based on the finite speed propagation property for the solution of the corresponding wave equation. We also discuss the relation between the Gaussian bounds and the finite speed propagation property. Using the wave e...

Robust Distributed Source Coding with Arbitrary Number of Encoders and Practical Code Design Technique

The robustness property can be added to DSC system at the expense of reducing performance, i.e., increasing the sum-rate. The aim of designing robust DSC schemes is to trade off between system robustness and compression efficiency. In this paper, after deriving an inner bound on the rate–distortion region for the quadratic Gaussian MDC based RDSC system with two encoders, the structure of...