Results on the minimization of the Dirichlet functional among semicartesian parametrizations
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Date
2015-08-07
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Abstract
We start to investigate the existence of conformal minimizers for the Dirichlet functional in the setting of the so-called semicartesian parametrizations, adapting to this context some techniques used in solving the classical Plateau's problem.
The final goal is to find area minimizing semicartesian parametrizations spanning a Jordan curve obtained as union of two graphs; this problem appeared in the study of the relaxed area functional for maps from the plane to the plane jumping on a line.
Description
The article is compsed of 18 pages and is recorded in PDF format
Keywords
Dirichlet energy, area-minimizing surfaces, semicartesian surfaces