A general quasilinear elliptic problem with variable exponents and Neumann boundary conditions for image processing

2025/02/28 by Maxim, Bogdan
#35A01 #35A02 #35B09 #35D30 #35J20 #35J62 #35J92 #98A08 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.20756

Abstract

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 surpass the lack of coercivity of the Euler-Lagrange functional with an innovative technique that has at its core the idea of showing that the minimum of the energy functional over a subset of the space W^1,p(x)(Ω) coincides with the global minimum. The obtained existence result applies to multiple-phase elliptic problems under remarkably weak assumptions.

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