arXiv subjects
Publications and source records attributed to Abhilash Sahu.
In this article, we show that $α$-fractal functions defined on Sierpiński gasket (denoted by $\triangle$) depend continuously on the parameters involved in the construction. In the latter part of this article, the continuous dependence of parameters on $α$-fractal functions defined on $\triangle$ is shown graphically.
In this paper, we have obtained bounds for the box dimension of graph of harmonic function on the Sierpiński gasket. Also we get upper and lower bounds for the box dimension of graph of functions that belongs to $\text{dom}(\mathcal{E}),$ that is, all finite energy functionals on the Sierpiński gasket. Further, we show the existence of fractal functions in the function space $\text{dom}(\mathcal{E})$ with the help of fractal interpolation functions. Moreover, we provide bounds for the box dimension of some functions that belong to the family of continuous functions and arise as fractal interpolation functions.
In this paper we study a system of boundary value problems involving weak p-Laplacian on the Sierpiński gasket in $\mathbb{R}^2$. Parameters $λ, γ, α, β$ are real and $1 1$ we show the existence of at least two nontrivial weak solutions to the system of equations for some $(λ,γ) \in \mathbb{R}^2.$
In this paper we study the following boundary value problem involving the weak p-Laplacian. \begin{equation*} \quad -M(\|u\|_{\mathcal{E}_p}^p)Δ_p u = h(x,u) \; \text{in}\; \mathcal{S}\setminus\mathcal{S}_0; \quad u = 0 \; \mbox{on}\; \mathcal{S}_0, \end{equation*} where $\mathcal{S}$ is the Sierpiński gasket in $\mathbb{R}^2$, $\mathcal{S}_0$ is its boundary. $M : \mathbb{R} \to \mathbb{R}$ defined by $M(t) = at^k +b$ and $a,b,k >0$ and $h : \mathcal{S} \times \mathbb{R} \to \mathbb{R}.$ We will show the existence of two nontrivial weak solutions to the above problem.