A boundary value problem for minimal Lagrangian graphs

On the Second Boundary Value Problem for a Class of Fully Nonlinear Flows I

“…By the above result, we can extend Brendle-Warren's theorem [1] to the case in (R n × R n , g π 4 ):…”

“…As same as the statement in [1], the range of c should be limited for the solvability of the equation (1.13) and the condition (1.18) reflect the issue in some way. On the other hand, in Section 3, we will prove that there exist universal constants µ 1 and µ 2 such that (λ 1 , λ 2 , · · · , λ n ) are always in Γ + ]µ 1 ,µ 2 [ under the flow.…”

“…By Theorem 1.1, we reprove the existence result on the second boundary value problem for special Lagrangian equations which belongs to S.Brendle and M.Warren. By [1] and [6], we present the similar special Lagrangian diffeomorphism problem in the following. The two convex domains Ω,Ω ⊂ R n with smooth boundary are fixed.…”

“…Using the continuity method of solving fully nonlinear elliptic equations with second boundary condition, S. Brendle and M. Warren [1] obtained the existence and uniqueness of the solution to (1.5). In [3], the first author studied the parabolic type special Lagrangian equation with second boundary condition:…”

“…is concerned, S. Brendle and M. Warren [1] proved the existence and uniqueness of the solution by the elliptic methods and the first author [3] obtained the existence of solution by the parabolic methods.…”