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

On the second boundary value problem for Lagrangian mean curvature equation

“…Theorem 1.3 presents an extension of the previous work on κ = 0 done by Brendle-Warren [9], Huang [10], Huang-Ou [11], Huang-Ye [12] and Chen-Huang-Ye [13].…”

“…As far as τ = π 2 is concerned, Brendle and Warren [9] proved the existence and uniqueness of the solution by the elliptic method, and the second author [10] obtained the existence of solution by the parabolic method. Then by the elliptic and parabolic method, the second author with Ou [11], Ye [12] [13] and Chen [13] proved the existence and uniqueness of the solution to (1.7) for 0 < τ < π 2 . For a smooth function f , Chen, Zhang and the third author [14] proved that if u satisfies…”

“…Now, by the continuity method, we can show that: Proof of Theorem 2.3. For each t ∈ [0, 1], consider By the main results in [11] and [12], (5.5) is solvable if t = 0. By Lemma 5.2, denote the closed subset X := {u ∈ C 2,α ( Ω) :…”

On the second boundary value problem for special Lagrangian curvature potential equation

“…Using the parabolic method, Schnürer and Smoczyk [11] also arrived at the existence of solutions to (1.1) for τ = 0. For further studies on the rest of 0 ≤ τ ≤ π 2 , see [1], [12] [13] and the references therein.…”

The Neumann boundary 问题 for $\boldsymbol{k}$-Hessian equations on compact manifolds

“…与此同 时, Chen 等 [23] 考察了对数 Monge-Ampère 方程-特殊 Lagrange 方程的 Neumann 边值问题, 得到了 该问题解的存在性结果. 相关的工作还有文献 [24]. 随后, Jiang 和 Trudinger [25][26][27] 研究了 k-Hessian 方程的斜微商边值问题解的存在性和正则性.…”