Indranil Chowdhury- PhD
- Professor (Assistant) at Indian Institute of Technology Kanpur
Indranil Chowdhury
- PhD
- Professor (Assistant) at Indian Institute of Technology Kanpur
About
11
Publications
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Introduction
My research areas concern Theory and Numerical analysis of Partial Differential Equations involving Nonlocal Operators.
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Publications
Publications (11)
![Initial conditions g1\documentclass[12pt]{minimal} \usepackage{amsmath}...](publication/385318877/figure/fig1/AS:11431281286956315@1730172435725/Initial-conditions-g1documentclass12ptminimal-usepackageamsmath_Q320.jpg)
We study discretizations of fractional fully nonlinear equations by powers of discrete Laplacians. Our problems are parabolic and of order \(\sigma \in (0,2)\) since they involve fractional Laplace operators \((-\Delta )^{\sigma /2}\). They arise e.g. in control and game theory as dynamic programming equations – HJB and Isaacs equation – and soluti...
There are few results on mean field game (MFG) systems where the PDEs are either fully nonlinear or have degenerate diffusions. This paper introduces a problem that combines both difficulties. We prove existence and uniqueness for a strongly degenerate, fully nonlinear MFG system by using the well-posedness theory for fully nonlinear MFGs establish...
We prove precise rates of convergence for monotone approximation schemes of fractional and nonlocal Hamilton–Jacobi–Bellman equations. We consider diffusion-corrected difference-quadrature schemes from the literature and new approximations based on powers of discrete Laplacians, approximations that are (formally) fractional order and second-order m...
We construct numerical approximations for Mean Field Games with fractional or nonlocal diffusions. The schemes are based on semi-Lagrangian approximations of the underlying control problems/games along with dual approximations of the distributions of agents. The methods are monotone, stable, and consistent, and we prove convergence along subsequenc...
We study monotone numerical schemes for nonlocal Isaacs equations, the dynamic programming equations of stochastic differential games with jump-diffusion state processes. These equations are fully-nonlinear non-convex equations of order less than $2$. In this paper they are also allowed to be degenerate and have non-smooth solutions. The main contr...
We derive C-1,C-sigma-estimate for the solutions of a class of non-local elliptic Bellman-Isaacs equations. These equations are fully nonlinear and are associated with infinite horizon stochastic differential game problems involving jump-diffusions. The non-locality is represented by the presence of fractional order diffusion term and we deal with...
The article is an attempt to investigate the issues of asymptotic analysis
for problems involving fractional Laplacian where the domains tend to become
unbounded in one-direction. Motivated from the pioneering work on second order
elliptic problems by Chipot and Rougirel, where the force functions are
considered on the cross section of domains, we...
We derive $C^{1+\sigma}$-estimate for a class of non-local elliptic Bellman
equations. These equations are fully nonlinear and are associated with infinite
horizon stochastic control/game problems involving jump-diffusions. The
non-locality is represented by the presence of fractional order diffusion term
and we deal with the particular case of $\f...
