A New Setting For Skyrme’s Problem

TL;DRAbstract

In [3] we gave some existence results for the general Skyrme’s problem, without any symmetry assumption. This problem arises as a natural model when searching to identify baryons as solitons in meson field theory. For more details about the physics motivation see [1,7,9,10]. It can be defined as follows. A class of functions ø : R 3 → S3, X,has to be defined so that the Skyrme’s energy functional 1 % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTduMaai % ikaiabfA6agjaacMcacqGH9aqpdaWdraqaaiaacYhacqGHhis0cqaH % vpGzaSqaaiaadkfadaahaaadbeqaaiaaiodaaaaaleqaniabgUIiYd % GccaGG8bWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaaiiFaiaadgea % caGGOaGaeqy1dyMaaiykaiaacYhadaahaaWcbeqaaiaaikdaaaGcca % WGKbGaamiEaiaacYcaaaa!4FE8! $$ \varepsilon (\Phi ) = \int_{{

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