Bernstein type theorems for some types of parabolic k-Hessian equations

ある種の放物型 k-Hessian 方程式に対する Bernstein 型定理

Nakamori Saori

We are concerned with the characterization of entire solutions to the parabolic k-Hessian equation of the form −utFk(D2u) = 1 in Rn ×(−∞, 0]. We prove that for 1 ≤ k ≤ n, any strictly convex-monotone solution u = u(x, t) ∈ C4,2(Rn × (−∞, 0]) to −utFk(D2u) = 1 in Rn × (−∞, 0] must be a linear function of t plus a quadratic polynomial of x, under some growth assumptions on u.

Mathematics [ 410 ]

eng

Saori Nakamori and Kazuhiro Takimoto; Uniqueness of boundary blowup solutions to k-curvature equation; Journal of Mathematical Analysis and Applications, 399 (2013), 496-504. (doi: 10.1016/j.jmaa.2012.10.021) references

Saori Nakamori and Kazuhiro Takimoto; A Bernstein type theorem for parabolic k-Hessian equations; Nonlinear Analysis: Theory, Methods & Applications, 117 (2015), 211-220. (doi: 10.1016/j.na.2015.01.010) references

[DOI] http://doi.org/10.1016/j.jmaa.2012.10.021 references

[DOI] http://doi.org/10.1016/j.na.2015.01.010 references

広島大学