Mathematical Sciences: Quasiconformal Analysis: Extensions and Applications

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PI: Manfredi DMS-9501561 Manfredi will investigate the interplay between nonlinear elasticity and function theory. He will attempt to bridge the gap between quasiregular mappings and mappings describing deformations of certain types of hyperelastic materials. Regularity up to the boundary of solutions to nonlinear elliptic systems that appear often in applications to non-Newtonian fluid mechanics will also be discussed. The significance of this research is the interconnections between areas of classical analysis and materials science. Partial differential equations form a basis for mathematical modeling of the physical world. The role of mathematical analysis is not so much to create the equations as it is to provide qualitative and quantitative information about the solutions. This may include answers to questions about uniqueness, smoothness and growth. In addition, analysis often develops methods for approximation of solutions and estimates on the accuracy of these approximations.