Genericity of Singular Behavior in Nonlinear Optimization Problems of Continuum Mechanics

Victor J. Mizel
Carnegie Mellon University
Department of Mathematical Sciences

It has been discovered that in some areas of continuum mechanics (broadly interpreted) anomalous singular behavior can arise. This leads to the possibility that engineering/metallurgical practice should be more conservatively formulated than traditional views suggest. The case is considerably strengthened if it can be shown that the singular behavior is generic in nature. Two such contexts will be discussed and the possible influence on related dynamical problems will be mentioned.