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

1982 ◽  
Author(s):  
E. DiBenedetto
Keyword(s):  
Weak Solutions ◽  
Elliptic Equations ◽  
Local Regularity ◽  
Degenerate Elliptic Equations ◽  
Regularity Of Weak Solutions ◽  
Degenerate Elliptic

scholarly journals Local regularity for concave homogeneous complex degenerate elliptic equations dominating the Monge–Ampère equation

2021 ◽  
Author(s):  
Soufian Abja ◽  
Guillaume Olive
Keyword(s):  
Elliptic Equations ◽  
Regularity Result ◽  
Nonlinear Elliptic Equations ◽  
Local Regularity ◽  
Degenerate Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Homogeneous Complex ◽  
Degenerate Elliptic ◽  
Monge Ampere

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.

scholarly journals A Note on Regularity of Solutions to Degenerate Elliptic Equations of Caffarelli-Kohn-Nirenberg Type

2003 ◽  
Vol 3 (4) ◽  
Author(s):  
Veronica Felli ◽  
Matthias Schneider
Keyword(s):  
Weak Solutions ◽  
Elliptic Equations ◽  
Hölder Continuity ◽  
Regularity Of Solutions ◽  
Degenerate Elliptic Equations ◽  
Holder Continuity ◽  
Degenerate Elliptic

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

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