Regularity of the stress field for degenerate and/or singular elliptic problems
Annales mathématiques Blaise Pascal, Volume 31 (2024) no. 1, pp. 83-135.

We investigate the regularity of the solutions to degenerate and/or singular elliptic equations. We prove the continuity of G(u) where u is a locally Lipschitz solution of divG(u)=λ in dimension two under some growth assumptions on G. Additionally, we establish a result that holds in any dimension, indicating that the separation between u and the degeneracy set of G is continuous.

Nous étudions la régularité des solutions d’équations elliptiques dégénérées et/ou singulières. Nous prouvons la continuité de G(u)u est une solution localement Lipschitz de divG(u)=λ en dimension deux sous certaines hypothèses de croissance sur G. De plus, nous établissons un résultat valable en toute dimension, indiquant que la séparation entre u et l’ensemble de dégénérescence de G est continue.

Published online:
DOI: 10.5802/ambp.427
Classification: 35B65, 35J62, 35J70, 35J75, 49N99
Keywords: Regularity, elliptic PDE, dimension two

Benjamin Lledos 1

1 Université de Toulouse Institut de Mathématiques de Toulouse CNRS UMR 5219 31062 Toulouse Cedex 9, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Benjamin Lledos. Regularity of the stress field for degenerate and/or singular elliptic problems. Annales mathématiques Blaise Pascal, Volume 31 (2024) no. 1, pp. 83-135. doi : 10.5802/ambp.427. https://ambp.centre-mersenne.org/articles/10.5802/ambp.427/

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