Prashanth K Srinivasan
Professor (H)
Room No.204
Email:
pras [ AT ] tifrbng [ DOT ] res [ DOT ] in
Office Phone:
+91 80 6695-3746
Research Interests
- Variational Methods
- Partial Differential Equations of Elliptic type
A brief description of research work
My major interest has been in the area of semi(quasi)linear elliptic equations, especially those involving critical growth nonlinearities. I have used techniques in Calculus of variations, regularity theory and geometric measure theory in my works. Broadly, my work has fallen under the following topics:
- Nonexistence Theorems and Blow-up analysis of Palais-Smale sequences for critical nonlinearity in \(\mathbb{R}^2\)
- Strong Comparison Principle for solutions of quasilinear equations
- Multiple solutions for \( p \)-Laplace equation in a ball
- Uniqueness of least energy solutions to the critical Neumann problem in \(\mathbb{R}^N \) , \( N ≥ 4 \)
- Perturbed Scalar curvature problem on \(\mathbb{S} ^ 2\) and the Perturbed \(Q\)-curvature problem on \( \mathbb{S}^N \); exact multiplicity result for the perturbed scalar curvature problem on \(\mathbb{S} ^N \) .
- Multiplicity results for exponential nonlinearities with a concave perturbation and convex-concave/singular type nonlinearities
- Simplicity of the principal eigenvalues obtained as Rayleigh quotient minima
- Isolated singularity for exponential type problems in two dimensions
- Sobolev versus smooth minimisers
- Bifurcation analysis for elliptic equations with a singular type nonlinearitiy
- Critical/subcritical classification of non-negative Schrodinger operators with singular potentials.