Mathematics Problem Archive

Prove the existence of energy minimizers for elastostatics for quasiconvex stored-energy functions $W$ satisfying $W(A)\to\infty$ as $\det A\to0^+$ ....

Prove or disprove that, under reasonable growth conditions on $W$, energy minimizers satisfy the weak Euler-Lagrange equations....

Justify the Ciarlet-Nečas minimization problem, or an appropriate modification, in situations involving smooth self-contact....

Prove or disprove uniqueness of sufficiently smooth equilibrium solutions for pure-displacement problems in homogeneous bodies homeomorphic to a ball ...

Develop local and global bifurcation theories for nonlinear elastostatics with mixed displacement-traction boundary conditions....

Clarify the status of models based on the fracture energy functional (2.31) in the source relative to classical fracture and nonlinear elastostatics....

Develop criteria for dynamic stability and instability of equilibria in nonlinear elasticity....

For the set of energy-minimizing gradients $K(\theta)$ defined in the source, determine its quasiconvex hull $K(\theta)^{qc}$ for $\theta\le\theta_c$....

Give a rigorous derivation of models of rods, plates, and shells from three-dimensional elasticity as thickness tends to zero....

For viscous incompressible flow in $\mathbb{R}^3\setminus B$ past a fixed obstacle $B$, with velocity approaching a nonzero constant vector at infinit...