By Luigi Ambrosio, Luis A. Caffarelli, Michael G. Crandall, Lawrence C. Evans, Nicola Fusco, Visit Amazon's Bernard Dacorogna Page, search results, Learn about Author Central, Bernard Dacorogna, , Paolo Marcellini, E. Mascolo
This quantity presents the texts of lectures given through L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco on the summer time direction held in Cetraro (Italy) in 2005. those are introductory reviews on present learn by way of global leaders within the fields of calculus of adaptations and partial differential equations. the themes mentioned are delivery equations for nonsmooth vector fields, homogenization, viscosity tools for the limitless Laplacian, susceptible KAM conception and geometrical features of symmetrization. A historic review of all CIME classes at the calculus of diversifications and partial differential equations is contributed through Elvira Mascolo.
Read or Download Calculus of variations and nonlinear partial differential equations: lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 27-July 2, 2005 PDF
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Extra info for Calculus of variations and nonlinear partial differential equations: lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 27-July 2, 2005
E. in the Eulerian form. A formal argument suggests that, given Pt , the velocity u should be deﬁned by ∂t ∇Pt∗ (∇Pt (x)) + ∇2 Pt∗ (∇Pt (x))J ∇Pt (x) − x . On the other hand, the a-priori regularity on ∇Pt (ensured by the convexity of Pt ) is a BV regularity, and it is still not clear how this formula could be rigorously justiﬁed. In this connection, an important intermediate step could be the proof of the W 1,1 regularity of the maps ∇Pt (see also , , , , ,  for the regularity theory of optimal transport maps under regularity assumptions on the initial and ﬁnal densities).
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