Affiliation:
1. Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste , via A. Valerio 12/1 , 34127 Trieste , Italy
Abstract
Abstract
This paper focuses on the existence and the multiplicity of classical radially symmetric solutions of the mean curvature problem:
−
div
∇
v
1
+
|
∇
v
|
2
=
f
(
x
,
v
,
∇
v
)
in
Ω
,
a
0
v
+
a
1
∂
v
∂
ν
=
0
on
∂
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
ℝ
N
{{\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.
Reference50 articles.
1. C. Corsato, C. De Coster, N. Flora, and P. Omari, Radial solutions of the Dirichlet problem for a class of quasilinear elliptic equations arising in optometry, Nonlinear Anal. 181 (2019), 9–23.
2. R. Finn, Remarks relevant to minimal surfaces, and to surfaces of prescribed mean curvature, J. Analyse Math. 14 (1965), 139–160.
3. H. Jenkins and J. Serrin, The Dirichlet problem for the minimal surface equation in higher dimensions, J. Reine Angew. Math. 229 (1968), 170–187.
4. J. Serrin, The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables, Philos. Trans. Roy. Soc. London Ser. A 264 (1969), 413–496.
5. O. A. Ladyzhenskaya and N. N. Ural’tseva, Local estimates for gradients of solutions of non-uniformly elliptic and parabolic equations, Comm. Pure Appl. Math. 23 (1970), 677–703.
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献