Mathematics Problem Archive

Find useful ways of verifying polyconvexity and quasiconvexity for stored-energy functions arising in anisotropic nonlinear elasticity....

Prove or disprove that, under reasonable growth conditions on $W$, an energy-minimizing deformation satisfies $\det Dy^*(x)\ge\varepsilon>0$....

Devise general methods for proving the existence of local but nonglobal minimizers and other weak equilibria in nonlinear elastostatics....

Develop a qualitative dynamics for dynamic theories of elasticity....

Establish the status of elasticity theory with respect to atomistic models....

For free-energy functions $\psi(A,\theta)$ of elastic crystals, determine boundary conditions under which the minimum is attained and conditions under...