相关论文: Extensions and their Minimizations on the Sierpins…

Aim of this note is to study the infinity Laplace operator and the corresponding Absolutely Minimizing Lipschitz Extension problem on the Sierpinski gasket in the spirit of the classical construction of Kigami for the Laplacian. We…

In this paper, we first characterize the finiteness of fractal interpolation functions (FIFs) on post critical finite self-similar sets. Then we study the Laplacian of FIFs with uniform vertical scaling factors on Sierpinski gasket (SG). As…

The number of independent sets is equivalent to the partition function of the hard-core lattice gas model with nearest-neighbor exclusion and unit activity. We study the number of independent sets $m_{d,b}(n)$ on the generalized Sierpinski…

In this paper we study a system of boundary value problems involving weak p-Laplacian on the Sierpi\'nski gasket in $\mathbb{R}^2$. Parameters $\lambda, \gamma, \alpha, \beta$ are real and $1<q<p<\alpha+\beta.$ Functions $a,b,h :…

We derive the complete asymptotic expansion in terms of powers of $N$ for the geodesic $f$-energy of $N$ equally spaced points on a rectifiable simple closed curve $\Gamma$ in ${\mathbb R}^p$, $p\geq2$, as $N \to \infty$. For $f$ decreasing…

Inspired by R. Bartnik's mass minimization problem in general relativity, we investigate a dual problem of maximizing the capacity among asymptotically flat extensions (with nonnegative scalar curvature) of some fixed two-dimensional…

Let $E$ be the Sierpinski gasket, i.e., the self-similar set generated by the IFS $\left \{f_a(x)=\frac{x+a}{q}: a\in \{(0,0), (0,1), (1,0)\}\right \}$. In paper, we provide a description of the following set for $2<q<3$ \begin{equation*}…

This paper studies presentations of the Sierpinski gasket as a final coalgebra for functors on several categories of metric spaces with additional designated points. The three categories which we study differ on their morphisms: one uses…

We study the analog of power series expansions on the Sierpinski gasket, for analysis based on the Kigami Laplacian. The analog of polynomials are multiharmonic functions, which have previously been studied in connection with Taylor…

We study the Hamiltonian of a two-dimensional log-gas with a confining potential $V$ satisfying the weak growth assumption -- $V$ is of the same order than $2\log|x|$ near infinity -- considered by Hardy and Kuijlaars [J. Approx. Theory,…

For a family of domains in the Sierpinski gasket, we study harmonic functions of finite energy, characterizing them in terms of their boundary values, and study their normal derivatives on the boundary. We characterize those domains for…

We extend and survey results in the theory of analysis on fractal sets from the standard Laplacian on the Sierpi\'nski gasket to the energy Laplacian, which is defined weakly by using the Kusuoka energy measure. We also extend results from…

This paper concerns the shape optimization problem of minimizing the ground state energy of the magnetic Dirichlet Laplacian with constant magnetic field among three-dimensional domains of fixed volume. In contrast to the two-dimensional…

Let $a>0,b>0$ and $V(x)\geq0$ be a coercive function in $\mathbb R^2$. We study the following constrained minimization problem on a suitable weighted Sobolev space $\mathcal{H}$: \begin{equation*}…

The paper deals with minimum energy problems in the presence of external fields with respect to the Riesz kernels $|x-y|^{\alpha-n}$, $0<\alpha<n$, on $\mathbb R^n$, $n\geqslant2$. For quite a general (not necessarily lower semicontinuous)…

Energy minimizing maps (E.M.M.s) play a central role in the calculus of variations, partial differential equations (PDEs), and geometric analysis. These maps are often embedded into $C^\infty$ Riemannian manifolds to minimize the Dirichlet…

We give a mathematically rigorous construction of a magnetic Schr\"odinger operator corresponding to a field with flux through finitely many holes of the Sierpinski Gasket. The operator is shown to have discrete spectrum accumulating at…

We study the number of connected spanning subgraphs $f_{d,b}(n)$ on the generalized Sierpinski gasket $SG_{d,b}(n)$ at stage $n$ with dimension $d$ equal to two, three and four for $b=2$, and layer $b$ equal to three and four for $d=2$. The…

We study the convergence of resistance metrics and resistance forms on a converging sequence of spaces. As an application, we study the existence and uniqueness of self-similar Dirichlet forms on Sierpinski gaskets with added rotated…

We prove existence and regularity of optimal shapes for the problem$$\min\Big\{P(\Omega)+\mathcal{G}(\Omega):\ \Omega\subset D,\ |\Omega|=m\Big\},$$where $P$ denotes the perimeter, $|\cdot|$ is the volume, and the functional $\mathcal{G}$…