Geodesic
Estimates on elliptic equations that hold only where the gradient is large
Journal of the European Mathematical Society, Tome 18 (2016) no. 6, pp. 1321-1338.

Voir la notice de l'article provenant de la source EMS Press

We consider a function which is a viscosity solution of a uniformly elliptic equation only at those points where the gradient is large. We prove that the Hölder estimates and the Harnack inequality, as in the theory of Krylov and Safonov, apply to these functions.
DOI : 10.4171/jems/614
Classification : 35-XX
Keywords: Degenerate elliptic equations, regularity, viscosity solutions 
@article{JEMS_2016_18_6_a4,
     author = {Cyril Imbert and Luis Silvestre},
     title = {Estimates on elliptic equations that hold only where the gradient is large},
     journal = {Journal of the European Mathematical Society},
     pages = {1321--1338},
     publisher = {mathdoc},
     volume = {18},
     number = {6},
     year = {2016},
     doi = {10.4171/jems/614},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/614/}
}
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Cyril Imbert; Luis Silvestre. Estimates on elliptic equations that hold only where the gradient is large. Journal of the European Mathematical Society, Tome 18 (2016) no. 6, pp. 1321-1338. doi : 10.4171/jems/614. http://geodesic.mathdoc.fr/articles/10.4171/jems/614/

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