NECESSARY AND SUFFICIENT CONDITIONS TO BERNSTEIN THEOREM OF A HESSIAN EQUATION
The Hessian quotient equations (0.1) Sk,l(D2u) ≡ SSkl((DD22uu)) = 1, ∀x ∈ Rn were studied for k−th symmetric elementary function Sk(D2u) of eigenvalues λ(D2u) of the Hessian matrix D2u, where 0 ≤ l < k ≤ n. For l = 0, (0.1) is reduced to a k−Hessian equation (0.2) Sk(D2u) = 1, ∀x ∈ Rn. Two quadra...
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| Format: | Article |
| Language: | English |
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American Mathematical Society
2022
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| Online Access: | View Fulltext in Publisher |