A Bernstein type theorem for parabolic k-Hessian equations

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 quadrat...

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Bibliographic Details
Published in:	Nonlinear analysis Vol. 117; pp. 211 - 220
Main Authors:	Nakamori, Saori, Takimoto, Kazuhiro
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01-04-2015
Subjects:	Bernstein type theorem Fully nonlinear equation Functions (mathematics) Mathematical analysis Nonlinearity Parabolic Hessian equation Pogorelov type lemma Polynomials Theorems 35K96 Pogorelov type lemma Fully nonlinear equation Bernstein type theorem Parabolic Hessian equation 35K55 35B08
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Summary:	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.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	0362-546X 1873-5215
DOI:	10.1016/j.na.2015.01.010