arXiv subjects
Publications and source records attributed to Ramya Dutta.
In this article we establish the radial symmetry of positive solutions of a p- Laplace equation in the Hyperbolic space, which is the Euler Lagrange equation of the p- Poincare Sobolev inequality in the Hyperbolic space. We will also establish the sharp decay of solution and its gradient and also investigate the question of existence of solution.
We prove sharp asymptotic estimates for the gradient of positive solutions to certain nonlinear $p$-Laplace equations in Euclidean space by showing symmetry and uniqueness of positive solutions to associated limiting problems.
Let $Ω$ be a bounded convex domain in $\mathbb{R}^n$ ($n \ge 2$). In this work, we prove that if there exists an integrable function $f$ such that it's Radon transform over $(n-1)$-dimensional hyperplanes intersecting the domain $Ω$ is a strictly positive function of distance to the nearest parallel supporting hyperplane to $Ω$, then $Ω$ is a ball and the function $f$ is a unique radial function about the centre of $Ω$.