Magnetostatic problems in fractal domains

2018/05/21 by Creo, Simone, Lancia, Maria Rosaria, Vernole, Paola +2
#28A80 #35J25 #35K15 #46E35 #47A07 #60J45 #65M15 #65M50 #65M60 #81Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Metric Geometry (math.MG) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1805.08262

Abstract

We consider a magnetostatic problem in a 3D "cylindrical" domain of Koch type. We prove existence and uniqueness results for both the fractal and pre-fractal problems and we investigate the convergence of the pre-fractal solutions to the limit fractal one. We consider the numerical approximation of the pre-fractal problems via FEM and we prove a priori error estimates. Some numerical simulations are also shown. Our long term motivation includes studying problems that appear in quantum physics in fractal domains.

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