Regularity of n/2-harmonic maps into spheres [Elektronische Ressource] / vorgelegt von Armin Schikorra

Regularity of n/2-harmonic maps into spheresVon der Fakult at fur Mathematik, Informatik und Naturwissenschaftender Rheinisch{Westf alischen Technischen Hochschule Aachenzur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften genehmigteDissertationvorgelegt vonDiplom{MathematikerArmin Schikorraaus Altenkirchen (Westerwald)Berichter: Prof. Dr. Heiko von der Mosel (RWTH Aachen)Prof. Dr. Pawe l Strzelecki (Uniwersytet Warszawski)Tag der mundlic hen Prufung: 22. September 2010Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfugbar.AbstractIn the present thesis, we consider critical points of the functional n 2 4E (v) := vnnRn nn n n2 2evaluated at points v2 H (R ) with the constraintjvj = 1 on some domain DR . Here, H (R ) denotes2 nthe fractional Sobolev space of all functions v2L (R ) such thatn ^ 2 n2j j v ()2L (R );^where () is the Fourier transform. We extend earlier results for evenn andn = 1 to arbitrary dimensionn2Nby proving H older continuity of critical points u of E .nAs for the proof, we adapt an approach by L. Tartar, which was used originally to prove Wente’s inequality, inorder to ensure the existence of compensation phenoma appearing in the Euler-Lagrange equations.In order to localize this e ect, we establish several localization results for nonlocal operators comparable to thefractional laplacian.