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ID 38523
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title alternative
ある種の放物型 k-Hessian 方程式に対する Bernstein 型定理
creator
Nakamori, Saori
NDC
Mathematics
abstract
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.
language
eng
nii type
Thesis or Dissertation
HU type
Doctoral Theses
DCMI type
text
format
application/pdf
text version
ETD
relation references
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)
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)
relation references URL
http://doi.org/10.1016/j.jmaa.2012.10.021
http://doi.org/10.1016/j.na.2015.01.010
grantid
甲第6738号
degreeGrantor
広島大学(Hiroshima University)
degreename Ja
博士(理学)
degreename En
Doctor of Science
degreelevel
doctoral
date of granted
2015-06-22
department
Graduate School of Science



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