The Free Boundary Value Problem of $\alpha $-Harmonic Maps Flow

Abstract

We study the $\alpha $-harmonic map flow with free boundary for the Sacks–Uhlenbeck functional on a compact Riemann surface with smooth boundary and prove that this flow exists globally for smooth initial data and converges to an $\alpha $-harmonic map with free boundary as $t\rightarrow \infty $.

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School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature