A class of elliptic systems with discontinuous variable exponents and [formula omitted] data for image denoising

Abstract

This paper investigates a class of elliptic systems consisting of the p(x)-Laplacian equation and the Poisson equation for image denoising. Under the assumption that p−>max{1,N3}, where p−≔essinfx∈Ωp(x) and N is the dimension of Ω, we prove the existence and uniqueness of weak solutions for the homogeneous Neumann boundary value problem with discontinuous variable exponent p(x) and L1 data. The proof, which is based on Schauder’s fixed-point theorem, also provides an iterative scheme for solving the system numerically. Experimental results illustrate that the proposed system with piecewise constant p(x) performs better than commonly used smooth p(x) in image denoising.