2024/05/14 by David Kalaj, Kalaj, David
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Complex Variables (math.CV) #Composite Material Mechanics #Elasticity and Material Modeling #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2405.08902
openalex publication_date 2024/05/14 · openalex created_date 2024/05/17 · openalex updated_date 2026/07/28
Let \mathbbA and \mathbbB be circular annuli in the complex plane and consider the Dirichlet energy integral of j-degree mappings between \mathbbA and \mathbbB. Then we minimize this energy integral. The minimizer is a j-degree harmonic mapping between annuli \mathbbA and \mathbbB provided it exits. If such a harmonic mapping does not exist, then the minimizer is still a j-degree mapping which is harmonic in \mathbbA'⊂ \mathbbA and it is a squeezing mapping in its complementary annulus \mathbbA''=\mathbbA∖ \mathbbA. Such a result is an extension of the certain result of Astala, Iwaniec and Martin \citeastala2010.