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• W2162688803 abstract "We study an energy minimizing sequence<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=${u_i}$><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math>in a fixed homotopy class of smooth maps from a<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$3$><mml:mn>3</mml:mn></mml:math>-manifold. After deriving an approximate monotonicity property for<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=${u_i}$><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math>and a continuous version of the Luckhaus lemma (Simon, 1996) on<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$S^2$><mml:msup><mml:mi>S</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>, we show that, passing to a subsequence,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=${u_i}$><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math>converges strongly in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$W^{1,2}$><mml:msup><mml:mi>W</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>topology wherever there is small energy concentration." @default.
• W2162688803 created "2016-06-24" @default.
• W2162688803 creator A5051533068 @default.
• W2162688803 date "2004-01-01" @default.
• W2162688803 modified "2023-09-25" @default.
• W2162688803 title "Minimizing energy among homotopic maps" @default.
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• W2162688803 doi "https://doi.org/10.1155/s0161171204305053" @default.
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