Seminar Title:
A study of nonlinear elliptic PDEs with Navier and Dirichlet boundary conditions
Seminar Type:
Synopsis Seminar
Department:
Mathematics
Speaker Name:
Rupali Kumari ( Rollno : 520ma1005)
Speaker Type:
Student
Venue:
Seminar Room(Department of Mathematics)
Date and Time:
30 Jun 2025 5:00pm
Contact:
Rasmita Kar
Abstract:
Our work is devoted to the analysis of elliptic boundary value problems within the framework
of weighted Sobolev spaces, with a particular focus on problems involving the biharmonic op
erator under the Navier boundary conditions. Weighted spaces naturally arise when studying
PDEs in nonhomogeneous media, domains with singularities, degenerate or singular coeffi
cients. Additionally, this work explores nonlinear operators of divergence form with Dirichlet
boundary conditions. Special attention is given to the equation with nonlinear p-Laplacian
operator. These problems introduce significant analytical challenges, stemming both from
the degeneracy and singularity introduced by the weights, and from the inherent nonlinearity
of the operators. The main contribution of our work include the establishment of existence,
uniqueness for various classes of boundary value problems. We also proved the properties
of solutions set for some problems. Appropriate functional settings and formulations are
developed, highlighting the interplay between the geometry of the domain, choice of weights
and the nature of the differential operators involved.