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Singular solutions to special Lagrangian equations with subcritical phases and minimal surface systems. (English) Zbl 1277.35125

Summary: 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.

MSC:

35D40 Viscosity solutions to PDEs
35B45 A priori estimates in context of PDEs
35J60 Nonlinear elliptic equations
35A20 Analyticity in context of PDEs
53A05 Surfaces in Euclidean and related spaces