A Class of De Giorgi Type and Hölder Continuity for Some Problems in Musielak-Orlicz-Sobolev Spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908770252095488 |
|---|---|
| author | Missaoui, Hlel Bahrouni, Anouar Ounaies, Hichem |
| author_facet | Missaoui, Hlel Bahrouni, Anouar Ounaies, Hichem |
| contents | In this paper, we introduce a new class of De Giorgi type functions, denoted by \(\mathcal{B}_{G(x,t)}\), and establish the Hölder continuity of its elements under suitable additional assumptions on the generalized \textnormal{N}-function \(G(x,t)\). As an application, we prove the Hölder continuity of solutions to quasilinear equations whose principal part is in divergence form with \(G(x,t)\)-growth conditions, including both critical and standard growth cases. The novelty of our work lies in the generalization of the Hölder continuity results previously known for variable exponent \cite[X, Fan and D. Zhao]{Fan1999} and Orlicz \cite[G. M. Lieberman]{Li1991} problems. Moreover, our results encompass a wide variety of quasilinear equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16392 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Class of De Giorgi Type and Hölder Continuity for Some Problems in Musielak-Orlicz-Sobolev Spaces Missaoui, Hlel Bahrouni, Anouar Ounaies, Hichem Analysis of PDEs In this paper, we introduce a new class of De Giorgi type functions, denoted by \(\mathcal{B}_{G(x,t)}\), and establish the Hölder continuity of its elements under suitable additional assumptions on the generalized \textnormal{N}-function \(G(x,t)\). As an application, we prove the Hölder continuity of solutions to quasilinear equations whose principal part is in divergence form with \(G(x,t)\)-growth conditions, including both critical and standard growth cases. The novelty of our work lies in the generalization of the Hölder continuity results previously known for variable exponent \cite[X, Fan and D. Zhao]{Fan1999} and Orlicz \cite[G. M. Lieberman]{Li1991} problems. Moreover, our results encompass a wide variety of quasilinear equations. |
| title | A Class of De Giorgi Type and Hölder Continuity for Some Problems in Musielak-Orlicz-Sobolev Spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.16392 |