We consider the smallest viscosity solution of the Hessian equation $S_k(D^2u) = f(u)$ in a k-convex domain, that becomes infinite at the boundary of the domain; here $S_k(D^2u)$ denotes the k-th elementary symmetric function of the eigenvalues of the Hessian matrix of the function $u$, for k ∈ {1, . . . , n}. We prove that if the domain is strictly convex and $f$ satisfies suitable assumptions, then the smallest solution is convex. We also establish asymptotic estimates for the behaviour of such a solution near the boundary.
Titolo: | Convexity and asymptotic estimates for large solutions of Hessian equations |
Autori di Ateneo: | |
Autori: | COLESANTI, ANDREA; FRANCINI, ELISA; SALANI, PAOLO |
Data di pubblicazione: | 2000 |
Rivista: | |
Volume: | 13 N. 10-12 |
Pagina iniziale: | 1459 |
Pagina finale: | 1472 |
Abstract: | We consider the smallest viscosity solution of the Hessian equation $S_k(D^2u) = f(u)$ in a k-convex domain, that becomes infinite at the boundary of the domain; here $S_k(D^2u)$ denotes the k-th elementary symmetric function of the eigenvalues of the Hessian matrix of the function $u$, for k ∈ {1, . . . , n}. We prove that if the domain is strictly convex and $f$ satisfies suitable assumptions, then the smallest solution is convex. We also establish asymptotic estimates for the behaviour of such a solution near the boundary. |
Handle: | http://hdl.handle.net/2158/345710 |
Appare nelle tipologie: | 1a - Articolo su rivista |
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