Revisiting the sub- and super-solution method for the classical radial solutions of the mean curvature equation

Open Mathematics

卷:18

Obersnel Franco¹  Omari Pierpaolo¹ 

[1] Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, via A. Valerio 12/1, 34127 Trieste, Italy;

关键词: prescribed mean curvature equation;    dirichlet;    neumann;    robin boundary conditions;    radial symmetry;    classical solution;    sub- and super-solutions;    35j62;    35j93;    35j25;    34c25;   

DOI  :  10.1515/math-2020-0097

来源: DOAJ

【 摘 要 】

This paper focuses on the existence and the multiplicity of classical radially symmetric solutions of the mean curvature problem:−div∇v1+|∇v|2=f(x,v,∇v)inΩ,a0v+a1∂v∂ν=0on∂Ω,\left\{\begin{array}{ll}-\text{div}\left(\frac{\nabla v}{\sqrt{1+|\nabla v{|}^{2}}}\right)=f(x,v,\nabla v)& \text{in}\hspace{.5em}\text{Ω},\\ {a}_{0}v+{a}_{1}\tfrac{\partial v}{\partial \nu }=0& \text{on}\hspace{.5em}\partial \text{Ω},\end{array}\right.with Ω\text{Ω} an open ball in ℝN{{\mathbb{R}}}^{N}, in the presence of one or more couples of sub- and super-solutions, satisfying or not satisfying the standard ordering condition. The novel assumptions introduced on the function f allow us to complement or improve several results in the literature.

【 授权许可】

Unknown