Continuity in two dimensions for a very degenerate elliptic equation
By Filippo Santambrogio, V. Vespri. 2009
55 citations recorded by the source corpus.
An elliptic equation ∇⋅(F(∇u))=f whose ellipticity strongly degenerates for small values of ∇u (say, F=0 on B(0,1)) is considered. The aim is to prove regularity for F(∇u). The paper proves a continuity result in dimension 2 and presents some applications.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3a858aa58bf451bdb054605b9d98949daa46ec6d
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Lorenzo Brasco
- Maria Colombo
- Guillaume Carlier
- Alessio Figalli
- Cristiana De Filippis
- Giuseppe Mingione
- Robert J. McCann
- Guido De Philippis
In Computational Theory and Mathematics
- Lorenzo Brasco
- Maria Colombo
- Alessio Figalli
- Guillaume Carlier
- Cristiana De Filippis
- Giuseppe Mingione
- Patrick Winkert
- Leszek Gasinski
In Mathematical Physics
- Lorenzo Brasco
- Maria Colombo
- Alessio Figalli
- Guillaume Carlier
- Patrick Winkert
- Leszek Gasinski
- Giuseppe Mingione
- Cristiana De Filippis
Citations in the corpus
- Regularity results for very degenerate elliptic equations (2014, background): “More precisely, there exist functions F satisfying our assumptions and H Lipschitz such that H(∇u) is not Hölder continuous for any exponent.”
- On certain anisotropic elliptic equations arising in congested optimal transport: Local gradient bounds (2014, background): “We also mention the papers [12, 24] where the continuity of 0 is proved.”