Abstract
We establish a sharp integrability condition on the partial derivatives of a mapping with L p-integrable distortion for some p>n− 1 to guarantee discreteness and openness. We also show that a mapping with exponentially integrable distortion and integrable Jacobian determinant is either constant or both discrete and open. We give an example demonstrating the preciseness of our criterion.
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Accepted May 2, 2001¶Published online October 1, 2001
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Kauhanen, J., Koskela, P. & Malý, J. Mappings of Finite Distortion:¶Discreteness and Openness. Arch. Rational Mech. Anal. 160, 135–151 (2001). https://doi.org/10.1007/s002050100162
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DOI: https://doi.org/10.1007/s002050100162