The exterior Dirichlet problem for Hessian quotient equations. (English) Zbl 1250.35098
Summary: In this paper, using a reverse MacLaurin inequality, we establish the existence theorem of the exterior Dirichlet problem for Hessian quotient equations with a stronger asymptotic behavior at infinity. When \(k\leq (n+1)/2\), we improve the result in [the second author, J. Math. Anal. Appl. 380, No. 1, 87–93 (2011; Zbl 1216.35032)] for \(S_{k,l}\) with \(k - l\geq 3\) to the result with any \(0\leq l\leq k\).
MSC:
| 35J60 | Nonlinear elliptic equations |
| 35D40 | Viscosity solutions to PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
Keywords:
Hessian quotient equations; exterior Dirichlet problem; reverse MacLaurin inequality; viscosity solutionsCitations:
Zbl 1216.35032References:
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