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 via L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco on the summer season direction held in Cetraro (Italy) in 2005. those are introductory stories on present study by means of international leaders within the fields of calculus of diversifications and partial differential equations. the subjects mentioned are shipping equations for nonsmooth vector fields, homogenization, viscosity tools for the countless Laplacian, susceptible KAM idea and geometrical elements of symmetrization. A historic assessment of all CIME classes at the calculus of adaptations 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
2). It is interesting to compare our characterization of Lagrangian ﬂows with the one given in . Heuristically, while the Di Perna-Lions one is based on the semigroup of transformations x → X(t, x), our one is based on the properties of the map x → X(·, x). 3. e. x. Then, Y (t, s, x) corresponds, in our notation, to the ﬂow X s (t, x) starting at time s (well deﬁned even for t < s if one has two-sided L∞ bounds on the divergence). In our setting condition (c) can be recovered as a consequence with the following argument: assume to ﬁx the ideas that s ≤ s ≤ T and deﬁne ˜ x) := X(t, X s (t, x) if t ∈ [s , s]; X s t, X s (s, x) if t ∈ [s, T ].
126 (2000), 1099–1115. 46. M. Cullen & W. Gangbo: A variational approach for the 2-dimensional semigeostrophic shallow water equations. Arch. Rational Mech. , 156 (2001), 241–273. 47. M. Cullen & M. Feldman: Lagrangian solutions of semigeostrophic equations in physical space. Preprint, 2003. 48. C. Dafermos: Hyperbolic conservation laws in continuum physics. Springer Verlag, 2000. 49. C. De Lellis: Blow-up of the BV norm in the multidimensional Keyﬁtz and Kranzer system. Duke Math. , 127 (2004), 313–339.
C. Evans & W. Gangbo: Diﬀerential equations methods for the MongeKantorovich mass transfer problem. Memoirs AMS, 653, 1999. 59. C. Evans, W. Gangbo & O. Savin: Nonlinear heat ﬂows and diﬀeomorphisms. Preprint, 2004. 60. H. Federer: Geometric measure theory, Springer, 1969. 61. M. Hauray: On Liouville transport equation with potential in BVloc . Comm. in PDE, 29 (2004), 207–217. 62. M. Hauray: On two-dimensional Hamiltonian transport equations with Lploc coeﬃcients. Ann. IHP Nonlinear Anal. Non Lin´eaire, 20 (2003), 625–644.
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 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