Details

Autor(en) / Beteiligte

• Bueno, Antonio
• López, Rafael

Titel

Radial solutions for equations of Weingarten type

Ist Teil von

• Journal of mathematical analysis and applications, 2023-01, Vol.517 (1), p.126575, Article 126575

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

2023

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper we study the linear Weingarten equation defined by the fully non-linear PDEadivDu1+|Du|2+bdetD2u(1+|Du|2)2=ϕ(11+|Du|2) in a domain Ω⊂R2, where ϕ∈C1([−1,1]) and a,b∈R. We approach the existence of radial solutions when Ω is a disk of small radius, giving an affirmative answer when the PDE is of elliptic type. In the hyperbolic case we show that no radial solution exists, while in the parabolic case we find explicitly all the solutions. In the elliptic case we prove uniqueness and symmetry results concerning the Dirichlet problem of such equation.