Singular solution to Special Lagrangian Equations
نویسندگان
چکیده
منابع مشابه
Singular Solutions to Special Lagrangian Equations with Subcritical Phases and Minimal Surface Systems
We construct singular solutions to special Lagrangian equations with subcritical phases and minimal surface systems. A priori estimate breaking families of smooth solutions are also produced correspondingly. A priori estimates for special Lagrangian equations with certain convexity are largely known by now.
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where λis are the eigenvalues of the Hessian D 2u. Namely, any global convex solution to (1.1) in R must be a quadratic polynomial. Recall the classical result, any global convex solution in R to the Laplace equation △u = λ1+ · · ·+λn = c or the Monge-Ampère equation log detD2u = log λ1+ · · ·+ log λn = c must be quadratic. Equation (1.1) originates from special Lagrangian geometry [HL]. The (L...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2010
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2010.05.001