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This publication comprises lecture notes of a chain of classes at the regularity conception of partial differential equations and variational difficulties, held in Pisa and Parma within the years 2009 and 2010. The members, Nicola Fusco, Tristan Rivière and Reiner Schätzle, supply 3 up to date and broad introductions to varied elements of contemporary Regularity conception pertaining to: mathematical modelling of skinny motion pictures and comparable loose discontinuity difficulties, research of conformally invariant variational difficulties through conservation legislation, and the research of the Willmore sensible.

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