Geometric Function Theory

Geometric Function Theory

This project includes study of spaces of functions and mappings with the emphasis on the properties needed in applications such as theory of Nonlinear Elasticity, Partial Differential Equations and Calculus of Variations. The natural problems studied in this area are the optimal condition that guarantee continuity (materiál cannot break and no cavities are created), null sets are mapped to null sets (materiál cannot be created from nothing), invertibility (interpenetration of matter), properties of the inverse mapping (backward deformation should be nice) and many others. Another aim of the study is the optimal conditions for various embeddings of function spaces.

Selected outputs

  • Csörnyei M., Hencl S., Malý J., Homeomorphisms in the Sobolev space $W^{1,n-1}$, J. Reine Angew. Math., 644 (2010), 221-235.

  • Hencl S., Sobolev homeomorphism with zero jacobian almost everywhere, J. Math. Pures Appl. 95 (2011), 444-458.

  • Cianchi A., Pick L., Slavíková L., Higher-order Sobolev embeddings and isoperimetric inequalities, Adv. Math. 273 (2015), 568-650.

Last change: February 10, 2018 23:20 
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