Research Projects & Grants
This page highlights my funded research projects and related mathematical initiatives. My current work is centered around nonlinear elliptic partial differential equations, fully nonlinear operators, principal eigenvalue problems, shape optimization, and applications to mathematical biology and optimal control.
Ongoing Funded Project
Shape Optimization of Principal Eigenvalue for Fully Nonlinear Operators: Theoretical and Geometric Advances on Pólya-Type Problems
Role: Principal Investigator
Funding Agency: Anusandhan National Research Foundation
(ANRF), Government of India
Scheme: ARG-MATRICS Research Grant
Host Institute: Visvesvaraya National Institute of
Technology Nagpur
Duration: 25 April 2026 – 24 April 2031
Total Grant: Rs. 30,00,000/-
This project investigates shape optimization problems for principal eigenvalues associated with fully nonlinear elliptic operators, with particular emphasis on Pucci extremal operators and related non-divergence form equations. The central theme is to understand how the geometry of a domain influences the principal eigenvalue in the fully nonlinear setting.
The project aims to develop theoretical and geometric advances related to Pólya-type spectral problems for fully nonlinear operators. It brings together tools from viscosity solution theory, nonlinear elliptic PDEs, principal eigenvalue problems, and geometric analysis of domains.
Some of the broad research directions include:
- principal eigenvalue problems for fully nonlinear elliptic operators;
- shape optimization and geometric inequalities for Pucci-type operators;
- Pólya-type problems in nonlinear and non-divergence form settings;
- symmetry, domain geometry, and eigenvalue minimization questions;
- viscosity solution methods for fully nonlinear spectral problems.
Related Research Directions
Alongside the funded project, I am also interested in collaborative research on existence, uniqueness, multiplicity, bifurcation, and regularity questions for nonlinear elliptic and parabolic PDEs. My broader research interests include singular nonlinearities, natural gradient growth, nonlinear boundary conditions, coupled systems, Hamilton– Jacobi– Bellman type equations, optimal control problems, and reaction– diffusion models arising in ecology and population dynamics.
For Students and Collaborators
Students and collaborators interested in fully nonlinear elliptic PDEs, principal eigenvalue problems, shape optimization, nonlinear analysis, or mathematical models in ecology and optimal control are welcome to contact me for possible research discussions.