Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations
Abstract In this paper, we consider the exterior Dirichlet problem of Hessian equations σ k ( λ ( D 2 u ) ) = g ( x ) $\sigma _{k}(\lambda (D^{2}u))=g(x)$ with g being a perturbation of a general positive function at infinity. By estimating the eigenvalues of the solution, we obtain the necessary an...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2022-06-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-022-01619-9 |
| Summary: | Abstract In this paper, we consider the exterior Dirichlet problem of Hessian equations σ k ( λ ( D 2 u ) ) = g ( x ) $\sigma _{k}(\lambda (D^{2}u))=g(x)$ with g being a perturbation of a general positive function at infinity. By estimating the eigenvalues of the solution, we obtain the necessary and sufficient conditions of existence of radial symmetric solutions with asymptotic behavior at infinity. |
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| ISSN: | 1687-2770 |