General least gradient problems with obstacle
General least gradient problems with obstacle
复制标题
障碍物的一般最小梯度问题
DOI：
10.1007/s00526-019-1635-8
复制
发表时间：
2019
影响因子：
2.1
通讯作者：
Moradifam, Amir
中科院分区：
文献类型：
--
作者：
Fotouhi, Morteza;Moradifam, Amir
We study existence, structure, uniqueness and regularity of solutions of the obstacle problem $$\begin{aligned} \inf _{u\in BV_f(\Omega )}\int _{\Omega }\phi (x,Du), \end{aligned}$$where B V f ( Ω ) = { u ∈ B V ( R n ) : u ≥ ψ in Ω and u | ∂ Ω = f | ∂ Ω } ,,is the obstacle, andis a convex, continuous and homogeneous function of degree one with respect to thevariable. We show that every minimizer of this problem is also a minimizer of the least gradient problem $$\begin{aligned} \inf _{u\in {\mathcal {A}}_f(\Omega )}\int _{{\mathbb {R}}^n}\phi (x,Du), \end{aligned}$$where A f ( Ω ) = { u ∈ B V ( Ω ) : u ≥ ψ , and u = f in Ω c } . Moreover, there exists a vector fieldTwithinwhich determines the structure of all minimizers of these two problems, andTis divergence free onfor any minimizeru. We also present uniqueness and regularity results that are based on maximum principles for minimal surfaces. Since minimizers of the least gradient problems with obstacle do not hit small enough obstacles, the results presented in this paper extend several results in the literature about least gradient problems without obstacle.
We study existence, structure, uniqueness and regularity of solutions of the obstacle problem $$\begin{aligned} \inf _{u\in BV_f(\Omega )}\int _{\Omega }\phi (x,Du), \end{aligned}$$where B V f ( Ω ) = { u ∈ B V ( R n ) : u ≥ ψ in Ω and u | ∂ Ω = f | ∂ Ω } ,,is the obstacle, andis a convex, continuous and homogeneous function of degree one with respect to thevariable. We show that every minimizer of this problem is also a minimizer of the least gradient problem $$\begin{aligned} \inf _{u\in {\mathcal {A}}_f(\Omega )}\int _{{\mathbb {R}}^n}\phi (x,Du), \end{aligned}$$where A f ( Ω ) = { u ∈ B V ( Ω ) : u ≥ ψ , and u = f in Ω c } . Moreover, there exists a vector fieldTwithinwhich determines the structure of all minimizers of these two problems, andTis divergence free onfor any minimizeru. We also present uniqueness and regularity results that are based on maximum principles for minimal surfaces. Since minimizers of the least gradient problems with obstacle do not hit small enough obstacles, the results presented in this paper extend several results in the literature about least gradient problems without obstacle.
登录
查看更多内容
最小梯度函数的 P 调和近似
DOI：
--
发表时间：
2005
期刊：
影响因子：
--
作者：
P. Juutinen
通讯作者：
P. Juutinen
DOI：
--
发表时间：
1998
期刊：
影响因子：
--
作者：
W. Ziemer;K. Zumbrun
通讯作者：
K. Zumbrun
浸没曲线空间上的分数 Sobolev 度量
DOI：
10.1007/s00526-018-1300-7
发表时间：
2017
影响因子：
2.1
作者：
Martin Bauer;Martins Bruveris;B. Kolev
通讯作者：
B. Kolev
DOI：
10.1137/10079241x
发表时间：
2010
期刊：
SIAM J. Appl. Math.
影响因子：
--
作者：
A. Nachman;A. Tamasan;A. Timonov
通讯作者：
A. Timonov
最小梯度函数和 1 次谐波函数
DOI：
--
发表时间：
2014
期刊：
影响因子：
--
作者：
J. M. Ruiz;J. Rossi;S. S. D. León
通讯作者：
S. S. D. León