Bernstein type theorems for some types of parabolic k-Hessian equations
Use this link to cite this item : https://ir.lib.hiroshima-u.ac.jp/00038523
| ID | 38523 |
| file | |
| title alternative | ある種の放物型 k-Hessian 方程式に対する Bernstein 型定理
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| creator |
Nakamori, Saori
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| NDC |
Mathematics
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| 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.
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| language |
eng
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| nii type |
Thesis or Dissertation
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| HU type |
Doctoral Theses
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| DCMI type | text
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| format | application/pdf
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| text version | ETD
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| 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)
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| relation references URL | http://doi.org/10.1016/j.jmaa.2012.10.021
http://doi.org/10.1016/j.na.2015.01.010
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| grantid | 甲第6738号
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| degreeGrantor | 広島大学(Hiroshima University)
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| degreename Ja | 博士(理学)
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| degreename En | Doctor of Science
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| degreelevel | doctoral
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| date of granted | 2015-06-22
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| department |
Graduate School of Science
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