Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider shape functionals obtained as minima on Sobolev spaces of classical integrals having smooth and convex densities, under mixed Dirichlet-Neumann boundary conditions.  propose a new approach for the computation of the second order shape derivative of such functionals, yielding a general existence and representation theorem. In particular,  consider the p-torsional rigidity functional for p ≥ 2.
['Guy Bouchitté', 'Ilaria Fragalà', 'Ilaria Lucardesi']
I am writing a research paper on a idea A variational method for second order shape derivatives
[{"from": "human", "value": "I am writing a research paper on a idea A variational method for second order shape derivatives"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider shape functionals obtained as minima on Sobolev spaces of classical integrals having smooth and convex densities, under mixed Dirichlet-Neumann boundary conditions.  propose a new approach for the computation of the second order shape derivative of such functionals, yielding a general existence and representation theorem. In particular,  consider the p-torsional rigidity functional for p \u2265 2."}]