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The Total Variation Flow in R N

Jan 31, 2023

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Andrea Colli
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Page 1: The Total Variation Flow in R N

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Page 2: The Total Variation Flow in R N

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Page 13: The Total Variation Flow in R N

N=ú�ÿ���ÿ A 6��ÿ kk � w ] _ § [ - - � �8790 Û - � �879080�¿Ð-�7<0 � � ?�� w ] _ § � ��- - � �8790 Û - � �87<080 � ¿ � � G � Ç ¿ ��à?�� � w ] _ § ¶ � ��- - � �87<0 Û - � �87<080 � ¿ � � G ¸\��i� 2 � �i� 2� � w ] _ § � Ç ¿ � � � 2��à?�� ô � w ] _ § �  ) - - � �8790 Û - � �87<080 � � ¿ � � �i� 2� � w ] _ § � Ç ¿ � � � 2� Ý

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Page 14: The Total Variation Flow in R N

A 6��þo÷�b � =�# � ��Â��¢þo÷5�Àþo÷�b�&¬L�.�M{�jÃ�+^54ÉÿVø¯& � =�' ñîW:ÿOü`� 2 úùø�ú�þ0ø� w ] _ § [ - D: Û : )�0�¿ �� � � 2� � .�A 6��þo÷�b¬&¬Ls& � M(N=ú�ÿX÷ � w ] _ § [ - - � �8790 Û )- � �87<080�¿ � � 2� � ?�A 6��þo÷�b � =�# � ��Â��¢þo÷5�Àþo÷�b�&¬Ls& � MÆs�ÿ 2 2÷ 2 4�����ÿ�ø�ú�þ0ø ) � û"÷ � -8# � ��Â���.`EHGIKJ"L -&' ) * 080"Mê ÒRÕëhÔÈì ~e× á�Û þ¾°²±�­aþ�®ÊÝ8ú�ú�塱cù`ú�ö6þ¼Þ ´ þ²³�ý�°¾�KÛ"±��\- )60 ´ °¾±¢¡�±�û�ÿ²Û¨Þ�°�þ � û5þnüDÿ®þ ´ ü � -8# � ��Â���.`E GIKJ"L -&' ) * 080�Ú�Û þ�ü- : )30 ´ °�±D¡�±�û�ÿ²Û¨Þ�°�þ � û5þnüDÿ®þ ´ ü�EHGIKJ"L -&' ) * 0²ß£ ¤�¥cõ¤ù,ï�| î�ô�| õTîûú ¶xrvo� ý?þ^ÿ����C ÒRÕ Õ ëK��×vØ þ/� ;: =pE{ô�-&' ) * 0 ±�ü;ý,³�þ�� ù"þ �KÛ þ¡°²�;Ý/ú6ü!�¬°�ú�³ ûR� ´ ú�üOú�å/�*�#�,±6üDýK�E$g��ß Ø þ/�S o � è ��= u è °�þ/�[ -_^�0\é � � y: ��- z�0 k z è ±�üDýij�þ/��¿X= � � -8# � ��Â���%V' ) * 0¼Ú ´ �KÛ�ÿ"ú�­t®R±3ÿ���°"ûÈ®Z® ú�ݲ� ´ üi7�ß�á�Û þnüw ] _ § [ - -3ÂU080�¿Ð-3ÂU0 Û wÃ: w ] _ § [ - 0�¿ �<� wÃ: w ] _ § ¿ k � � -���- 080 � -�Þ�?30� Û w Ã: w ] _ § z ª�Ç ¿-��- 0 � w ] _ § [ - D: 0�¿Ð-&��0 ÝJ3å ´ üj±3ý3ý ´ � ´ ú6üï��= u Æ � G -&' ),0 è �KÛ þ�üj�KÛ þ[þ � ûh±�³ ´ �;Þ�Ûú�³�ý�° ´ ü(��¦`$&��ß6J"üÄ®R±�ݲ� ´ ÿ�û"³ ±�Ý è ´ °v±�üuþ�üH�;Ý8úN®ÊÞÄ°nú�³ û%� ´ ú6üú�å��*�#��ß+�Ý8ú�ú�å/ß ß üTü`��Z­ÿyÔ��Rü�ø�ø�ú�þ0ø���û�ü\ A 2 4�þoü�ü � G M(N=ú�ÿX÷kk � w ] _ § [ - 0�¿ � w ] _ § ��- 0 � ¿ � w ] _ § [ - 0�¿ �

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Page 15: The Total Variation Flow in R N

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