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About My Thesis:

• Title of Thesis: On Qualitative Properties of Solutions to Nonhomogeneous Elliptic Equations ( Link )

• Description: This thesis investigates qualitative properties of solutions to nonhomogeneous quasilinear elliptic equations, focusing on either establishing regularity results or using these regularity properties to derive symmetry, comparison principles, and multiplicity of solutions. The work considers Dirichlet problems involving three operators: the (p,q)-Laplacian, the mixed local–nonlocal operator, and the fractional (p,q)-Laplacian. The main questions addressed include:

Radial symmetry and multiplicity for the (p,q)-Laplacian with singular and bounded nonlinearities.

Gradient Hölder regularity for the mixed local–nonlocal operator when the nonlinearity is singular and depends on the distance to the boundary.

Existence and multiplicity of non-negative solutions for mixed local–nonlocal problems with singular, subcritical, or critical nonlinearities.

Weighted Hölder boundary regularity for the fractional (p,q)-Laplacian with bounded right-hand side.

I successfully defended my thesis in September 2025.

• Thesis Examiners: Dr Mousumi Bhakta and Dr Marius Ghergu.

Personal Details:

• Nationality: Indian

• Gender: Male

• Age: 29

• Languages: Bengali (native), English (fluent), Hindi (proficient)

• Typesetting: LaTeX

• Programming: C++ and Python (basic; B.Sc. coursework)