C(1 + Alpha) Local Regularity of Weak Solutions of Degenerate Elliptic Equations.

1982 ◽  
Author(s):  
E. DiBenedetto
Author(s):  
Soufian Abja ◽  
Guillaume Olive

AbstractIn this paper, we establish a local regularity result for $$W^{2,p}_{{\mathrm {loc}}}$$ W loc 2 , p solutions to complex degenerate nonlinear elliptic equations $$F(D^2_{\mathbb {C}}u)=f$$ F ( D C 2 u ) = f when they dominate the Monge–Ampère equation. Notably, we apply our result to the so-called k-Monge–Ampère equation.


2003 ◽  
Vol 3 (4) ◽  
Author(s):  
Veronica Felli ◽  
Matthias Schneider

AbstractWe establish Hölder continuity of weak solutions to degenerate critical elliptic equations of Caffarelli-Kohn-Nirenberg type.


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