Geodesic
Solvability of Hessian quotient equations in exterior domains
Canadian journal of mathematics, Tome 77 (2025) no. 1, pp. 118-148

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DOI

In this paper, we study the Dirichlet problem of Hessian quotient equations of the form $S_k(D^2u)/S_l(D^2u)=g(x)$ in exterior domains. For $g\equiv \mbox {const.}$, we obtain the necessary and sufficient conditions on the existence of radially symmetric solutions. For g being a perturbation of a generalized symmetric function at infinity, we obtain the existence of viscosity solutions by Perron’s method. The key technique we develop is the construction of sub- and supersolutions to deal with the non-constant right-hand side g.
DOI : 10.4153/S0008414X23000834
Mots-clés : Hessian quotient equations, exterior Dirichlet problem, radially symmetric solutions, asymptotic behavior, necessary and sufficient conditions 
Dai, Limei; Bao, Jiguang; Wang, Bo. Solvability of Hessian quotient equations in exterior domains. Canadian journal of mathematics, Tome 77 (2025) no. 1, pp. 118-148. doi: 10.4153/S0008414X23000834
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     title = {Solvability of {Hessian} quotient equations in exterior domains},
     journal = {Canadian journal of mathematics},
     pages = {118--148},
     year = {2025},
     volume = {77},
     number = {1},
     doi = {10.4153/S0008414X23000834},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000834/}
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