Zobrazeno 1 - 10
of 68
pro vyhledávání: '"Fotouhi, Morteza"'
For a given constant $\lambda > 0$ and a bounded Lipschitz domain $D \subset \mathbb{R}^n$ ($n \geq 2$), we establish that almost-minimizers of the functional $$ J(\mathbf{v}; D) = \int_D \sum_{i=1}^{m} \left|\nabla v_i(x) \right|^p+ \lambda \chi_{\{
Externí odkaz:
http://arxiv.org/abs/2311.09073
We study temperature distribution in a heat conducting problem, for a system of p-Laplace equation, giving rise to a free boundary.
Externí odkaz:
http://arxiv.org/abs/2309.12794
In this paper, we study the classification of Lipschitz global solutions for a two-phase $p$-Laplace Bernoulli problem, subject to a mild assumption. Specifically, we focus on the scenario where the interior two-phase points of the global solution ar
Externí odkaz:
http://arxiv.org/abs/2306.04656
We show that any minimizer of the well-known ACF functional (for the $p$-Laplacian) is a viscosity solution. This allows us to establish a uniform flatness decay at the two-phase free boundary points to improve the flatness, that boils down to $C^{1,
Externí odkaz:
http://arxiv.org/abs/2301.11775
Autor:
Fotouhi, Morteza, Shahgholian, Henrik
In this paper we consider a weakly coupled $p$-Laplacian system of a Bernoulli type free boundary problem, through minimization of a corresponding functional. We prove various properties of any local minimizer and the corresponding free boundary.
Externí odkaz:
http://arxiv.org/abs/2301.02236
Autor:
Fotouhi, Morteza, Koch, Herbert
In this paper we are concerned with higher regularity properties of the elliptic system \[ \Delta\mathbf{u}= |\mathbf{u}|^{q-1}\mathbf{u}\chi_{\{|\mathbf{u}|>0\}},\qquad\mathbf{u}=(u^1,\dots,u^m) \] for $0\leq q<1$. We show analyticity of the regular
Externí odkaz:
http://arxiv.org/abs/2212.13321
In this work we address graph based semi-supervised learning using the theory of the spatial segregation of competitive systems. First, we define a discrete counterpart over connected graphs by using direct analogue of the corresponding competitive s
Externí odkaz:
http://arxiv.org/abs/2211.16030
Publikováno v:
In Journal of Differential Equations 15 December 2024 412:447-473
Autor:
Fotouhi Morteza, Shahgholian Henrik
Publikováno v:
Advances in Nonlinear Analysis, Vol 13, Iss 1, Pp 355-387 (2024)
In this article, we consider a weakly coupled pp-Laplacian system of a Bernoulli-type free boundary problem, through minimization of a corresponding functional. We prove various properties of any local minimizer and the corresponding free boundary.
Externí odkaz:
https://doaj.org/article/ba86c89ecd5f4deb9d598505ec9e4df0
In this paper we study the following parabolic system \begin{equation*} \Delta \u -\partial_t \u =|\u|^{q-1}\u\,\chi_{\{ |\u|>0 \}}, \qquad \u = (u^1, \cdots , u^m) \ , \end{equation*} with free boundary $\partial \{|\u | >0\}$. For $0\leq q<1$, we p
Externí odkaz:
http://arxiv.org/abs/2106.04135