Necessary and sufficient conditions to Bernstein theorem of a Hessian equation
The Hessian quotient equations \begin{equation} S_{k,l}(D^2u)\equiv \frac {S_k(D^2u)}{S_l(D^2u)}=1, \ \ \forall x\in {\mathbb {R}}^n \end{equation} were studied for k-th symmetric elementary function S_k(D^2u) of eigenvalues \lambda (D^2u) of the Hessian matrix D^2u, where 0\leq l
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| Veröffentlicht in: | Transactions of the American Mathematical Society 2022-07, Vol.375 (7), p.4873-4892 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | The Hessian quotient equations \begin{equation} S_{k,l}(D^2u)\equiv \frac {S_k(D^2u)}{S_l(D^2u)}=1, \ \ \forall x\in {\mathbb {R}}^n \end{equation} were studied for k-th symmetric elementary function S_k(D^2u) of eigenvalues \lambda (D^2u) of the Hessian matrix D^2u, where 0\leq l |
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| ISSN: | 0002-9947 1088-6850 |
| DOI: | 10.1090/tran/8686 |