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Room No. 107
Office phone +91 80 6695 3728
Email Id debraj -at- math.tifrbng.res.in
Research Interests
My research is in the area of Complex Analysis in Several Variables. I have been exploring the regularity of the Cauchy-Riemann equations on domains with piecewise Levi-Flat and singular boundaries. The problem of solving the Cauchy-Riemann equations (also known as the dbar equation) is equivalent to construction of holomorphic functions.
Although this problem is well-understood in a domain whose boundary satisfies certain convexity conditions, there are several classes of interesting domains for which little is known about the boundary regularity of the solutions. Recently, in collaboration with Professor Mei Chi Shaw of the University of Notre Dame, we have been able to understand the blow up of the solutions of the Cauchy-Riemann equations in a well-known classical domain in two variables, called the "Hartogs' Triangle", and have obtained weighted Sobolev estimates for the solutions.
