Regularity of Solutions of Two-Dimensional Monge-Ampere Equations

1988 ◽  
Vol 307 (1) ◽  
pp. 271 ◽  
Author(s):  
Friedmar Schulz ◽  
Liang-Yuan Liao
Keyword(s):  
Regularity Of Solutions ◽  
Two Dimensional ◽  
Monge Ampere

Characterizing Two-Dimensional Maps Whose Jacobians Have Constant Eigenvalues

2003 ◽  
Vol 46 (3) ◽  
pp. 323-331 ◽  
Author(s):  
Marc Chamberland
Keyword(s):  
Nonlinear Pdes ◽  
Two Dimensional ◽  
Real Analytic ◽  
Monge Ampere

AbstractRecent papers have shown that C1 maps whose Jacobians have constant eigenvalues can be completely characterized if either the eigenvalues are equal or F is a polynomial. Specifically, F = (u, v) must take the formfor some constants a, b, c, d, e, f , α, β and a C1 function ϕ in one variable. If, in addition, the function ϕ is not affine, thenThis paper shows how these theorems cannot be extended by constructing a real-analytic map whose Jacobian eigenvalues are ±1/2 and does not fit the previous form. This example is also used to construct non-obvious solutions to nonlinear PDEs, including the Monge—Ampère equation.

scholarly journals C1,α regularity of solutions to parabolic Monge-Ampére equations

2012 ◽  
Vol 134 (4) ◽  
pp. 1051-1087 ◽  
Author(s):  
Panagiota Daskalopoulos ◽  
Ovidiu Savin
Keyword(s):  
Regularity Of Solutions ◽  
Monge Ampere
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