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Title of Journal: manuscripta math

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Abbravation: manuscripta mathematica

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Springer-Verlag

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10.1016/0196-9781(86)90232-9

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1432-1785

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Stability of flows associated to gradient vector f

Authors: Luigi Ambrosio Stefano Lisini Giuseppe Savaré
Publish Date: 2006/07/08
Volume: 121, Issue: 1, Pages: 1-50
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Abstract

In this paper we address the problem of stability of flows associated to a sequence of vector fields under minimal regularity requirements on the limit vector field that is supposed to be a gradient We apply this stability result to show the convergence of iterated compositions of optimal transport maps arising in the implicit time discretization with respect to the Wasserstein distance of nonlinear evolution equations of a diffusion type Finally we use these convergence results to study the gradient flow of a particular class of polyconvex functionals recently considered by Gangbo Evans and Savin We solve some open problems raised in their paper and obtain existence and uniqueness of solutions under weaker regularity requirements and with no upper bound on the jacobian determinant of the initial datum

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  1. A stability criterion for nonparametric minimal submanifolds
  2. Harmonic maps and asymptotic Teichmüller space
  3. On the backward uniqueness property for the heat equation in two-dimensional conical domains
  4. Minoration de la hauteur de Néron-Tate sur les surfaces abéliennes
  5. Willmore submanifolds of the Möbius space and a Bernstein-type theorem
  6. A positivity property of the Satake isomorphism
  7. Homological characterization of lean algebras
  8. Reduction of structure for torsors over semilocal rings
  9. Common divisors of elliptic divisibility sequences over function fields
  10. Finitistic dimensions of semiprimary rings
  11. Extending Elliptic Curve Chabauty to higher genus curves
  12. The Sp 3 -grassmannian and duality for prime Fano threefolds of genus 9
  13. Existence and compactness for the $${\overline{\partial}}$$ -Neumann operator on q-convex domains
  14. The normalization constant of a certain invariant measure on GL n ()
  15. Tropical descendant Gromov–Witten invariants
  16. A Harnack inequality for the quasi-minima of scalar integral functionals with general growth conditions
  17. Cut loci and conjugate loci on Liouville surfaces
  18. A sphere theorem on locally conformally flat even-dimensional manifolds
  19. On the class numbers of certain Hilbert class fields
  20. The zeros of certain weakly holomorphic Drinfeld modular forms
  21. Icosahedral representations and elliptic curves
  22. On entire functions whose derivatives are¶integer-valued on geometric progressions
  23. Perversité et variation
  24. On linear combinations of special values of L -functions
  25. Irrationalité de certaines sommes de séries
  26. Deformations of Koszul Artin–Schelter Gorenstein algebras
  27. On positive definite hermitian forms
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