A general quasilinear elliptic problem with variable exponents and Neumann boundary conditions for image processing
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916646762840064 |
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| author | Maxim, Bogdan |
| author_facet | Maxim, Bogdan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20756 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A general quasilinear elliptic problem with variable exponents and Neumann boundary conditions for image processing Maxim, Bogdan Analysis of PDEs 35A01, 35A02, 35B09, 35D30, 35J20, 35J62, 35J92, 98A08 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. |
| title | A general quasilinear elliptic problem with variable exponents and Neumann boundary conditions for image processing |
| topic | Analysis of PDEs 35A01, 35A02, 35B09, 35D30, 35J20, 35J62, 35J92, 98A08 |
| url | https://arxiv.org/abs/2502.20756 |