Research Statement
My research focuses on mean Hadamard inequalities and constrained variational problems motivated by topics in nonlinear elasticity.
Research Areas
Calculus of Variations
Existence and explicit construction of minimisers to variational problems.
Functional Analysis
Bounds for optimal constants in functional inequalities.
Nonlinear Elasticity
Integral functionals with polyconvex integrands and partial differential inclusions.
Current Projects
Conditions for the Non-Negativity of Excess Functionals in Constrained Variational Problems
Construction of explciit examples of mean Hadamard inequalities and minimisers of the Dirichlet energy in a Jacobian constrained class.
A Lower Bound for the Dirichlet Energy in a Class of Jacobian Constrained Maps
Establishing lower bounds for the Dirichlet energy functional subject to a Jacobian contraint and Dirichlet boundary conditions.
Research Impact
My research has developed new techiques for constructing explicit minimisers for functionals of a polyconvex integrand and Jacobian constrained variational problems. In doing so, I have been able to make progress on an open problem in elasticity and construct novel bounds for several inequalities in functional and harmonic analysis.