Mathematics Problem Archive
Showing 1-8 of 8 problems
Some Open Problems in Elasticity — Testing convexity conditions
v1.3 research notesFind useful ways of verifying polyconvexity and quasiconvexity for stored-energy functions arising in anisotropic nonlinear elasticity....
Some Open Problems in Elasticity — Regularity of minimizers
v1.3 research notesDetermine when the minimizer $y^*$ in Theorem 2.1 of the source is smooth....
Some Open Problems in Elasticity — A positive Jacobian bound
v1.3 research notesProve or disprove that, under reasonable growth conditions on $W$, an energy-minimizing deformation satisfies $\det Dy^*(x)\ge\varepsilon>0$....
Some Open Problems in Elasticity — Nonglobal local minimizers
v1.3 research notesDevise general methods for proving the existence of local but nonglobal minimizers and other weak equilibria in nonlinear elastostatics....
Some Open Problems in Elasticity — Qualitative dynamics
v1.3 research notesDevelop a qualitative dynamics for dynamic theories of elasticity....
Some Open Problems in Elasticity — Atomistic foundations
v1.3 research notesEstablish the status of elasticity theory with respect to atomistic models....
Some Open Problems in Elasticity — Elastic-crystal free energies
v1.3 research notesFor free-energy functions $\psi(A,\theta)$ of elastic crystals, determine boundary conditions under which the minimum is attained and conditions under...
Finite-dimensional dynamics for two-dimensional Navier–Stokes
v1.3 research notesIs the global attractor of the periodically forced two-dimensional Navier–Stokes equations conjugate to a smooth finite-dimensional dynamical system? ...