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

Bogdan Maxim

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arXiv · 2502.20756

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

Bogdan Maxim

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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 $W^{1,p(x)}(\Omega)$ coincides with the global minimum. The obtained existence result applies to multiple-phase elliptic problems under remarkably weak assumptions.

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Bogdan Maxim. 2025-02-28. A general quasilinear elliptic problem with variable exponents and Neumann boundary conditions for image processing. https://arxiv.org/abs/2502.20756

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