Prasun Roychowdhury

About

My research focuses on functional inequalities in both discrete and continuous settings. In particular, I study Hardy, Poincaré, and Rellich-type inequalities on negatively curved manifolds. My work also involves criticality theory, stochastic incompleteness, viscous Hamilton–Jacobi equations, and the Gelfand equation. In addition, I investigate spectral properties and eigenvalue problems for nonlinear operators in Euclidean spaces, with recent emphasis on the stability of eigenvalues under domain perturbations. More recently, I have developed an interest in tools from harmonic analysis, including maximal function estimates and John–Nirenberg-type inequalities for general capacities, especially those related to Choquet integrals. I am currently studying stability phenomena for various functional inequalities.

Employment

• Indian Institute of Technology Hyderabad Assistant Professor
  2026 - Present
• Waseda University JSPS Postdoctoral Researcher
  2026 - 2026
• Kerala School of Mathematics Visiting Assistant Professor
  2025 - 2026
• University of Milano-Bicocca Postdoc
  2024 - 2025
• National Center for Theoretical Sciences Postdoc
  2022 - 2024
• Indian Institute of Technology Delhi Research Associate
  2022 - 2022
• IISER Pune Senior Research Fellow
  2022 - 2022

Education

• IISER Pune PhD
  2017 - 2022
• IIT Kanpur MSc
  2015 - 2017
• Jadavpur University BSc
  2012 - 2015

Projects & Funding

Projects & funding information is unavailable.

Publications (15)

• Extremizer Stability of Higher-Order Hardy–Rellich Inequalities for Baouendi–Grushin Vector Fields
  The Journal of Geometric Analysis 2026 DOI: 10.1007/s12220-026-02550-6
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• Critical, stability and higher-order analysis for Hardy type inequalities on Cartan–Hadamard manifolds
  Mathematische Zeitschrift 2025 DOI: 10.1007/s00209-025-03853-0
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• The Capacitary John–Nirenberg Inequality Revisited
  Advances in Calculus of Variations 2025 DOI: 10.1515/acv-2025-0022
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• One-dimensional integral Rellich type inequalities
  Eurasian Mathematical Journal 2025 DOI: 10.32523/2077-9879-2025-16-1-86-93
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• Improvement of the discrete Hardy inequality
  Bulletin des Sciences Mathématiques 2024 DOI: 10.1016/j.bulsci.2024.103468
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• Multidimensional Frank–Laptev–Weidl improvement of the hardy inequality
  Proceedings of the Edinburgh Mathematical Society 2024 DOI: 10.1017/s0013091523000780
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• Stochastic completeness and L^1-Liouville property for second-order elliptic operators
  Discrete and Continuous Dynamical Systems - S 2024 DOI: 10.3934/dcdss.2022138
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• Classification of radial solutions to −Δ_g u = e^u on Riemannian models
  Journal of Differential Equations 2023 DOI: 10.1016/j.jde.2023.03.009
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• Improved Poincaré-Hardy inequalities on certain subspaces of the Sobolev space
  Proceedings of the American Mathematical Society 2023 DOI: 10.1090/proc/16357
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• Generalized principal eigenvalues on ℝ^d of second order elliptic operators with rough nonlocal kernels
  Nonlinear Differential Equations and Applications NoDEA 2023 DOI: 10.1007/s00030-022-00821-z
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