arXiv subjects

M. S. Indulekha

Publications and source records attributed to M. S. Indulekha.

3 recordsLinked to original sources

arXiv2025

Motion of Elastic Thin Films by Evaporation-Condensation in the Dewetting Regime

In this work, we show the short-time existence of solutions of the evolution equations that represent the solid state dewetting of thin films through evaporation-condensation as a two dimensional sharp interface variational model. The evolution law is established as the $L^2$ gradient flow of surface energies in the presence of epitaxial strain. The main novelty is the presence of moving contact lines when the film formation is governed by the evaporation-condensation method.

math.AP↗

arXiv2023

Parameter estimates and a uniqueness result for double phase problem with a singular nonlinearity

We consider the boundary value problem $-Δ_p u_λ-Δ_q u_λ=λg(x) u_λ^{-β}$ in $Ω$ , $u_λ=0$ on $\partial Ω$ with $u_λ>0$ in $Ω.$ We assume $Ω$ is a bounded open set in $\mathbb{R}^N$ with smooth boundary, $1<p<q<\infty$, $β\in [0,1),$ $g$ is a positive weight function and $λ$ is a positive parameter. We derive an estimate for $u_λ$ which describes its exact behavior when the parameter $λ$ is large. In general, by invoking appropriate comparison principles, this estimate can be used as a powerful tool in deducing the existence, non-existence and multiplicity of positive solutions of nonlinear elliptic boundary value problems. Here, as an application of this estimate, we obtain a uniqueness result for a nonlinear elliptic boundary value problem with a singular nonlinearity.

math.AP↗

arXiv2022

Strong comparison principle for a p-Laplace equation involving singularity and its applications

In this paper we prove a strong comparison principle for radially decreasing solutions $u,v\in C_{0}^{1,α}(\Bar{B_R})$ of the singular equations $-Δ_p u-\frac{1}{u^δ}=f(x)$ and $-Δ_p v-\frac{1}{v^δ}=g(x)$ in $B_R$. Here we assume that $ 1 2$ a counterexample is provided where the strong comparison principle is violated. As an application of strong comparison principle, we prove a three solution theorem for p-Laplace equation and illustrate with an example.

math.AP↗