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Mousomi Bhakta

Publications and source records attributed to Mousomi Bhakta.

40 records · Page 3Linked to original sources
arXiv2013

Semilinear elliptic equations admitting similarity transformations

In this paper we study the equation $-Δu+ρ^{-(α+2)}h(ρ^αu)=0$ in a smooth bounded domain $Ω$ where $ρ(x)=\textrm{dist}\,(x,\partial Ω)$, $α>0$ and $h$ is a non-decreasing function which satisfies Keller-Osserman condition. We introduce a condition on $h$ which implies that the equation is subcritical, i.e. the corresponding boundary value problem is well posed with respect to data given by finite measures. Under additional assumptions on $h$ we show that this condition is necessary as well as sufficient. We also discuss b.v. problems with data given by positive unbounded measures. Our results extend results of \cite{MV1} treating equations of the form $-Δu+ρ^βu^q=0$ with $q>1$, $β>-2$.

math.AP↗
arXiv2012

Reduced limit for semilinear boundary value problems with measure data

We study boundary value problems for semilinear elliptic equations of the form $-Δu+g\circ u=μ$ in a smooth bounded domain $Ω\subset R^N$. Let $\{μ_n\}$ and $\{τ_n\}$ be sequences of measure in $Ω$ and $\partial Ω$ respectively. Assume that there exists a solution $u_n$ of the equation with $μ=μ_n$ subject to boundary data $τ_n$. Further assume that the sequences of measures converge in a weak sense to $μ$ and $τ$ respectively and $\{u_n\}$ converges to $u$ in $L^1(Ω)$. In general $u$ is not a solution of the boundary value problem with data $(μ,τ)$. However there exist measures $(μ^*,τ^*)$ such that $u$ satisfies the equation with $μ$ replaced by $μ^*$ and with $u=τ^*$ on the boundary. The pair $(μ^*,τ^*)$ is called the reduced limit of the sequence $\{(μ_n,τ_n)\}$. We investigate the relation between the weak limit and the reduced limit and the dependence of the latter on the sequence.

math.AP↗
arXiv2011

Poincaré Sobolev equations in the Hyperbolic space

We study the a priori estimates,existence/nonexistence of radial sign changing solution, and the Palais-Smale characterisation of the problem $-\De_{\Bn}u - \la u = |u|^{p-1}u, u\in H^1(\Bn)$ in the hyperbolic space $\Bn$ where $1<p\leq\frac{N+2}{N-2}$. We will also prove the existence of sign changing solution to the Hardy-Sobolev-Mazya equation and the critical Grushin problem.

math.AP↗