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Qualitative Properties and Symmetry of Quasilinear Elliptic Equations

Mr Ramya Dutta (TIFR CAM, Bangalore) PhD Thesis defence
Speaker
Mr Ramya Dutta (TIFR CAM, Bangalore) PhD Thesis defence
When Sep 11, 2023
from 02:00 PM to 03:00 PM
Where Ground Floor Auditorium (006)
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Abstract :  In this talk we will primarily focus on quasilinear elliptic equations which are Euler-Lagrange equations of Sobolev Inequalities in Euclidean or Hyperbolic space. In one of my work, we have established sharp decay estimates for solutions to the quasilinear Hardy-Sobolev-Maz'ya equation in the Euclidean space. As an application of such estimates we establish the existence of positive solutions to a Brezis-Nirenberg problem with sub-linear perturbations of Hardy-Sobolev equation in a smooth bounded domain containing the origin under a suitable notion of positivity for the perturbations. In another work, we have established sharp decay estimates of positive solutions to the Euler-Lagrange equation of the Poincare-Sobolev inequality in Hyperbolic space and established Hyperbolic symmetry of the same by employing the Alexandrov moving plane method. We also discuss some existence and non-existence results for the same.


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