2004/12/30 by Joy Ko
Mathematics · #Characterization (materials science) #Geometric Analysis and Curvature Flows #Hausdorff distance #Hausdorff space #Locally compact space #Measure (data warehouse) #Nonlinear Partial Differential Equations #Order (exchange) #Space (punctuation) #Spectral Theory in Mathematical Physics #Translation (biology) #math.AP #msc:35M10 #msc:35Q99
paper · pdf · doi:10.1088/0951-7715/18/6/014
43 pages, 2 figures
arxiv created 2004/12/30 · openalex publication_date 2005/09/16 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
We establish a framework to construct a global solution in the space of finite energy to a general form of the Landau–Lifshitz–Gilbert equation in . Our characterization yields a partially regular solution, smooth away from a two dimensional locally finite Hausdorff measure set. This construction relies on approximation by discretization, using the special geometry to express an equivalent system whose highest order terms are linear and the translation of the machinery of linear estimates on the fundamental solution from the continuous setting into the discrete setting. This method is quite general and accommodates a larger class of geometries involving targets that are closed smooth surfaces.