Weighted Poincar� inequalities for H�rmander vector fields and local regularity for a class of degenerate elliptic equations

1995 ◽  
Vol 4 (4) ◽  
pp. 361-375 ◽  
Author(s):  
B. Franchi ◽  
G. Lu ◽  
R. L. Wheeden
Keyword(s):  
Elliptic Equations ◽  
Vector Fields ◽  
Local Regularity ◽  
Degenerate Elliptic Equations ◽  
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 Existence results for nonlinear degenerate elliptic equations with lower order terms

2020 ◽  
Vol 10 (1) ◽  
pp. 301-310
Author(s):  
Weilin Zou ◽  
Xinxin Li
Keyword(s):  
Lower Order ◽  
Elliptic Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Regularity Of Solutions ◽  
Degenerate Elliptic Equations ◽  
Degenerate Elliptic ◽  
Initial Boundary Value ◽  
Lower Order Terms ◽  
Nonlinear Degenerate

Abstract In this paper, we prove the existence and regularity of solutions of the homogeneous Dirichlet initial-boundary value problem for a class of degenerate elliptic equations with lower order terms. The results we obtained here, extend some existing ones of [2, 9, 11] in some sense.

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