Year: 2014
Type: article
Abstract: Aim of this paper is to prove necessary and sufficient conditions on the geometry of a domain |$\Omega \subset \mathbb {R} ^n$| in order that the homogeneous Dirichlet problem for the infinity-Laplace equation in |$\Omega$| with constant source term admits a viscosity solution depending only on the distance from |$\partial \Omega$|. This problem was previously addressed and studied by Buttazzo and Kawohl [7]. In the light of some geometrical achievements reached in our recent paper [14], we revisit the results obtained in [7] and we prove strengthened versions of them, where any regularity assumption on the domain and on the solution is removed. Our results require a delicate analysis based on viscosity methods. In particular, we need to build suitable viscosity test functions, whose construction involves a new estimate of the distance function |$d_{\partial \Omega }$| near singular points.
DOI: 10.1093/imrn/rnu204
Authors: Graziano Crasta, Ilaria Fragalà
Institution: Politecnico di Milano
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952755557